Does a black hole necessarily contain a singularity?

Does a black hole necessarily contain a singularity?

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I'm basing this hypothesis on the theories around how an outside observer watching something fall into a black hole will never actually see the thing pass the event horizon. And secondly that from the perspective of the thing falling in, the surrounding universe would accelerate to see the end of the universe.

On that second point, the "end of the universe" from my understanding would be up until the black hole evaporates.

So the question. Is it possible for an event horizon to form; not necessarily from a singularity, but merely from there being enough compressed mass existing within the boundaries that an event horizon forms?

The implication from this if it has any merit would be in my opinion, that there are no singularities currently in existence and that there indeed might never be one, because currently I don't understand how something "inside" a black hole is capable of moving at all (I assume that to do so mass would need to move faster than light), suggesting that the entirety of a stellar remnant's mass is stuck in place both inside and on the surface of the event horizon.

EDIT: Re-reading that last paragraph I've confused myself a little, mass wouldn't necessarily be "stuck", but if it did move at all, it would be moving light speed, which is a paradox in itself?

Yes, an event horizon will form once escape velocity exceeds the speed of light. It does not necessarily require a singularity inside it.

However, there is no known physics that would allow any non-point-like object to exist inside an event horizon. It is hard to see how any traditional forces would be able to support an object in such case, and for quantum mechanics we simply do not have the theory that'd be valid in such high gravitational field.

Does every black hole contain a singularity? Does sound travel faster in space? Does the influence of gravity extend out forever? Galaxies look stationary, so why do scientists say that they rotate? Have aliens ever visited earth? Have astronomers ever observed a violet shift like they have blue shifts and red shifts? How bright is a laser beam when viewed from the side? How can astronomers know things for certain since they only look at space from one vantage point? How can there be anything left in the universe? Don't black holes suck everything in? How can you cancel out the jolt of a quick start? How can you tell a black hole made out of antimatter from a black hole made out of matter? How do space probes make it past the asteroid belt without crashing into asteroids? How do space ships fly faster than light?

Ohm's Law is a formula used to calculate the relationship between voltage, current and resistance in an electrical circuit. To students of electronics, Ohm's Law (E = IR) is as fundamentally important as Einstein's Relativity equation (E = mc²) is to physicists. E = I x R.


Every Black Hole Contains a New Universe

At the center of spiral galaxy M81 is a supermassive black hole about 70 million times more massive than our sun.

NASA/CXC/Wisconsin/D.Pooley & CfA/A.ZezasNASA/ESA/CfA/A.Zezas NASA/JPL-Caltech/CfA/J.Huchra et al. NASA/JPL-Caltech/CfA

Inside Science Minds presents an ongoing series of guest columnists and personal perspectives presented by scientists, engineers, mathematicians, and others in the science community showcasing some of the most interesting ideas in science today. The opinions contained in this piece are those of the author and do not necessarily reflect those of Inside Science nor the American Institute of Physics and its Member Societies.

(ISM) -- Our universe may exist inside a black hole. This may sound strange, but it could actually be the best explanation of how the universe began, and what we observe today. It's a theory that has been explored over the past few decades by a small group of physicists including myself.

Successful as it is, there are notable unsolved questions with the standard big bang theory, which suggests that the universe began as a seemingly impossible "singularity," an infinitely small point containing an infinitely high concentration of matter, expanding in size to what we observe today. The theory of inflation, a super-fast expansion of space proposed in recent decades, fills in many important details, such as why slight lumps in the concentration of matter in the early universe coalesced into large celestial bodies such as galaxies and clusters of galaxies.

But these theories leave major questions unresolved. For example: What started the big bang? What caused inflation to end? What is the source of the mysterious dark energy that is apparently causing the universe to speed up its expansion?

The idea that our universe is entirely contained within a black hole provides answers to these problems and many more. It eliminates the notion of physically impossible singularities in our universe. And it draws upon two central theories in physics.

The first is general relativity, the modern theory of gravity. It describes the universe at the largest scales. Any event in the universe occurs as a point in space and time, or spacetime. A massive object such as the Sun distorts or "curves" spacetime, like a bowling ball sitting on a canvas. The Sun's gravitational dent alters the motion of Earth and the other planets orbiting it. The sun's pull of the planets appears to us as the force of gravity. The second is quantum mechanics, which describes the universe at the smallest scales, such as the level of the atom. However, quantum mechanics and general relativity are currently separate theories physicists have been striving to combine the two successfully into a single theory of "quantum gravity" to adequately describe important phenomena, including the behavior of subatomic particles in black holes.

A 1960s adaptation of general relativity, called the Einstein-Cartan-Sciama-Kibble theory of gravity, takes into account effects from quantum mechanics. It not only provides a step towards quantum gravity but also leads to an alternative picture of the universe. This variation of general relativity incorporates an important quantum property known as spin. Particles such as atoms and electrons possess spin, or the internal angular momentum that is analogous to a skater spinning on ice.

In this picture, spins in particles interact with spacetime and endow it with a property called "torsion." To understand torsion, imagine spacetime not as a two-dimensional canvas, but as a flexible, one-dimensional rod. Bending the rod corresponds to curving spacetime, and twisting the rod corresponds to spacetime torsion. If a rod is thin, you can bend it, but it's hard to see if it's twisted or not.

Spacetime torsion would only be significant, let alone noticeable, in the early universe or in black holes. In these extreme environments, spacetime torsion would manifest itself as a repulsive force that counters the attractive gravitational force coming from spacetime curvature. As in the standard version of general relativity, very massive stars end up collapsing into black holes: regions of space from which nothing, not even light, can escape.

Here is how torsion would play out in the beginning moments of our universe. Initially, the gravitational attraction from curved space would overcome torsion's repulsive forces, serving to collapse matter into smaller regions of space. But eventually torsion would become very strong and prevent matter from compressing into a point of infinite density matter would reach a state of extremely large but finite density. As energy can be converted into mass, the immensely high gravitational energy in this extremely dense state would cause an intense production of particles, greatly increasing the mass inside the black hole.

The increasing numbers of particles with spin would result in higher levels of spacetime torsion. The repulsive torsion would stop the collapse and would create a "big bounce" like a compressed beach ball that snaps outward. The rapid recoil after such a big bounce could be what has led to our expanding universe. The result of this recoil matches observations of the universe's shape, geometry, and distribution of mass.

In turn, the torsion mechanism suggests an astonishing scenario: every black hole would produce a new, baby universe inside. If that is true, then the first matter in our universe came from somewhere else. So our own universe could be the interior of a black hole existing in another universe. Just as we cannot see what is going on inside black holes in the cosmos, any observers in the parent universe could not see what is going on in ours.

The motion of matter through the black hole's boundary, called an "event horizon," would only happen in one direction, providing a direction of time that we perceive as moving forward. The arrow of time in our universe would therefore be inherited, through torsion, from the parent universe.

Finally, torsion could be the source of "dark energy," a mysterious form of energy that permeates all of space and increases the rate of expansion of the universe. Geometry with torsion naturally produces a "cosmological constant," a sort of added-on outward force which is the simplest way to explain dark energy. Thus, the observed accelerating expansion of the universe may end up being the strongest evidence for torsion.

2 Answers 2

The important quantity associated with a black hole is the event horizon area. The volume contained inside is not what one would think of as $V = 4pi r^3/3$. More on the volume later. The important quantitiy is the area of the event horizon. The reason is that from the perspective of an exterior observer this is the limit of observation. Everything that falls into the black hole is observed to have its observed time intervals on a clock dilated or slowed as radiation it emits is red shifted arbitrarily far.

The Schwarzschild metric for a nonrotating black hole of mass $M$ gives the line element $ ds^2 = left(1 - frac<2m> ight)dt^2 - left(1 - frac<2m> ight)^<-1>dr^2 – r^2dOmega^2

m = GM/c^2 . $ For null rays we have the interval is zero $ds = 0$ and we proceed to compute the clock time $t$ on a standard coordinate frame of a very distant observer for the time it takes a photon to radially escape from some distance $R$ form a black hole $ int^Tdt = int_R^infty left(1 - frac<2m> ight)dr = R - 2m ln(R - 2m) $ clearly this becomes infinite as $R ightarrow 2m$. Physically this means that everything that made the black hole, including the original star that imploded into it are “pasted” right above the event horizon. It is as if the black hole has a geological layer cake structure of everything that went into it. Notice there is no reference at all to anything in the interior. The observer on the outside, which is the wise place to remain if you wish to keep living, witnesses everything about the black hole as pinned on the event horizon, and this is one basis for the holographic principle.

All of the stuff that composes the black hole forms the entropy of the black hole. The Bekenstein entropy for the area of a black hole event horizon $ S = k

The interior of a black hole is only accessible to those who enter it. This is at least the case for a classical black hole. For a quantum black hole there may be some fluctuations of the horizon which make quantum information of a black hole a superposition of states outside and inside. I will not go into that for now. For the pure Schwarzschild black hole the Penrose diagram The event horizon as seen by an observer in our universe is on the right. Once you cross the horizon it splits and the horizon separating the interior of the black hole from our universe and the other horizon separating the other universe from the interior grow apart. In this eternal black hole diagram, which is a sort of mathematical idealization, the horizons grow infinitely far apart. This means the spatial region in the interior grows, and becomes infinitely large at the singularity $r = 0$.

I could go further in how this mathematical idealization of the eternal black hole is perturbed by the collapsing star and by Hawking radiation. The imploding surface of a star will cut this diagram in half and the region between the material surface and the horizon will grow arbitrarily. Hawking radiation in addition cuts off the size of the distance between the collapsing surface and the horizon, or between these two split horizons. The scale of this has to do with the quantum Poincare recurrence and quantum complexity of the system, which gets us into a huge area of current research.

What is happening in the interior of a black hole is then a curiosity, and we will never know what happens in the interior of a large black hole. They are too far away, which is a good thing, and the classical nature of them makes access to the interior impossible. For quantum black holes, or more likely QCD analogus of AdS/black holes, we might be able to make inferences from quantum superposition of exterior and interior states.

10 Answers 10

But if you want to nit pick, I could argue that when a star collapses to form a BH, it first forms a horizon before the singularity forms (cannot form a "naked singularity"). And since time inside the horizon is essentially frozen with respect to that of an observer outside, the singularity NEVER forms. Yet from the point of view of the collapsing star, the singularity forms in about a millisecond after the horizon.

In classical General Relativity, once an event horizon forms, every particle inside that event horizon will inevitably travel in the direction of the center of the black hole. This is what is meant by "gravitational collapse" and how matter comes to form a singularity in the center- no matter how small it is, or how close to the center it is, nothing can prevent it from approaching ever closer to the center. From the point of view of the object itself, it does reach the center in a finite time.

In some more exotic theories of physics, such as string theory or loop quantum gravity, the quantized nature of space and time comes to the rescue and prevents a singularity from forming, so a maximum, finite density is reached and an equilibrium is maintained in the center. This is similar conceptually to what you describe, but still a more exotic and much, much denser material than neutron star-stuff.

The density we're talking about here would be approximately one Planck Mass per cubic Planck Length, in other words 2.176 51 × 10^−8 kg / (1.616 199 × 10^−35 m)^3

= 5.15556^96 kg/m^3, where neutron star material is "only" (roughly) 10^18 kg/m^3.

In either case, however, outside the event horizon, the black hole can be treated mathematically and observationally as a simple singularity, so for observational calculations, there is no "value added" in worrying about the inner workings of the black hole. The theorem describing this is colloquially called "Black holes have no hair." This theorem was proven and coined by John Wheeler, the same physicist who coined the phrase "black hole" in the first place.

Does a black hole necessarily contain a singularity? - Astronomy

If at the beginning of the universe we had a singularity does that mean that every black hole has the potential to create a universe as we know it?

No. A singularity is really more a mathematical concept than a physical entity. It's true that the math describing both black holes and the Big Bang contain singularities, but they are not related. Also, a black hole only a mass a few times the mass of our Sun, or in the case of the those at the centers of galaxies, a couple million Suns. The Universe is obviously quite a lot more massive.

This page was last updated June 27, 2015.

About the Author

Laura Spitler

Laura Spitler was a graduate student working with Prof. Jim Cordes. After graduating in 2013, she went on to a postdoctoral fellowship at the Max Planck Institute in Bonn, Germany. She works on a range of projects involving the time variability of radio sources, including pulsars, binary white dwarfs and ETI. In particular she is interested in building digital instruments and developing signal processing techniques that allow one to more easily identify and classify transient sources.

Stunning image of black hole reveals mysterious jets ‘blowing matter thousands of lightyears into space’

A NEW image of a black hole has been unveiled, revealing the vortex of magnetic chaos surrounding it.

The snap released by scientists this week gives a closer look at how the supermassive M87 black hole interacts with the matter surrounding it.

It's the sharpest image yet of the cosmic monster, which lies at the centre of the M87 galaxy some 55million light years from Earth.

The Event Horizon Telescope (EHT) team released the first image of a black hole in 2019, revealing a bright ring-like structure with a dark central region described as the black hole's shadow.

Researchers observed images of magnetic fields at the black hole's edge, where some matter falls in.

Meanwhile, other matter is being blown into space in the form of bright, powerful jets that extend at least 5,000 light years away, beyond the galaxy in which the black hole resides.

Using the same data as for their first image, the collaboration with University College London (UCL) analysed polarised light around the black hole – light whose waves are vibrating in one direction only.

The light becomes polarised when it is emitted in hot regions of space that are magnetised.

By looking at how it has become polarised, astronomers can learn about the material that produced it.

The new evidence brings researchers a step closer to understanding how these mysterious jets are produced, and how magnetic fields appear to act to keep hot gas out of the black hole, helping it resist gravity's pull.

Co-author and UCL astronomer Dr Ziri Younsi said: "These ground-breaking measurements provide us with exciting new insights into the physical processes by which black holes feed on matter, and how they are able to power such prodigious relativistic outflows as astrophysical jets.

"In particular, they hint at the role played by magnetic fields in these processes."

Dr Jason Dexter, of the University of Colorado, Boulder, US, said: "The observations suggest that the magnetic fields at the black hole's edge are strong enough to push back on the hot gas and help it resist gravity's pull.

"Only the gas that slips through the field can spiral inwards to the event horizon."

The EHT is an international collaboration set up to image a black hole by linking eight ground-based radio telescopes globally to make an Earth-sized virtual telescope with unprecedented sensitivity and resolution.

The resolution is sharp enough to measure an orange on the Moon from Earth.

The black hole in the image is located in a galaxy called Messier 87, or M87. It has a mass 6.5billion times that of the Sun.

The bright jets of energy and matter produced by a black hole are one of the galaxy's most mysterious features.

What is a black hole? The key facts

What is a black hole?

  • A black hole is a region of space where absolutely nothing can escape
  • That's because they have extremely strong gravitational effects, which means once something goes into a black hole, it can't come back out
  • They get their name because even light can't escape once it's been sucked in – which is why a black hole is completely dark

What is an event horizon?

  • There has to be a point at which you're so close to a black hole you can't escape
  • Otherwise literally everything in the universe would have been sucked into one
  • The point at which you can no longer escape from a black hole's gravitational pull is called the event horizon
  • The event horizon varies between different black holes, depending on their mass and size

What is a singularity?

  • The gravitational singularity is the very centre of a black hole
  • It's a one-dimensional point that contains an incredibly large mass in an infinitely small space
  • At the singularity, space-time curves infinitely and the gravitational pull is infinitely strong
  • Conventional laws of physics stop applying at this point

How are black holes created?

  • Most black holes are made when a supergiant star dies
  • This happens when stars run out of fuel – like hydrogen – to burn, causing the star to collapse
  • When this happens, gravity pulls the centre of the star inwards quickly, and collapses into a tiny ball
  • It expands and contracts until one final collapse, causing part of the star to collapse inward thanks to gravity, and the rest of the star to explode outwards
  • The remaining central ball is extremely dense, and if it's especially dense, you get a black hole

Most matter close to the edge of a black hole falls in, but some of the surrounding particles escape moments before capture.

They're then blown far out into space in the form of jets.

Astronomers have relied on different models of how matter behaves near the black hole to better understand this process.

But they still do not know exactly how jets larger than the galaxy are launched from its central region, which is as small in size as the Solar System, nor how exactly matter falls into the black hole.

Researchers say the observations provide new information about the structure of the magnetic fields just outside the black hole.

They found that only theoretical models featuring strongly magnetised gas can explain what they are seeing at the event horizon.

The new observations are described in two papers published in The Astrophysical Journal Letters.

Answers and Replies

"We show that the singularity is replaced by a bounce at which quantum effects are important and that the extent of the region at the bounce where one departs from classical general relativity depends on the initial data."

Good suggestion Shalayka! is a recent paper of Gambini Pullin and Campiglia.
Jim Graber, you ask "Has anything been published?" Plenty has been published in that general direction. here are some references. This is far from complete. I am excluding papers that deal only with the horizon or the exterior. This is a sample of loop papers having to do with the black hole interior.

A fair number of these papers were published in Physical Review Letters or in Physical Review D. [Broken]

1) Quantum geometry and the Schwarzschild singularity.
Abhay Ashtekar (Penn State U. & Potsdam, Max Planck Inst.) , Martin Bojowald (Potsdam, Max Planck Inst. & Penn State U.) . IGPG-05-09-01, AEI-2005-132, Sep 2005. 31pp.
Published in Class.Quant.Grav.23:391-411,2006.
e-Print: gr-qc/0509075
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 48 times

2) Black hole evaporation: A Paradigm.
Abhay Ashtekar (Penn State U.) , Martin Bojowald (Potsdam, Max Planck Inst. & Penn State U.) . IGPG04-8-4, AEI-2004-072, Apr 2005. 18pp.
Published in Class.Quant.Grav.22:3349-3362,2005.
e-Print: gr-qc/0504029
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 39 times

3) A Black hole mass threshold from non-singular quantum gravitational collapse.
Martin Bojowald (Potsdam, Max Planck Inst.) , Rituparno Goswami (Tata Inst.) , Roy Maartens (Portsmouth U., ICG) , Parampreet Singh (Penn State U.) . AEI-2005-020, IGPG-05-3-3, Mar 2005. 4pp.
Published in Phys.Rev.Lett.95:091302,2005.
e-Print: gr-qc/0503041
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 34 times

4) Nonsingular black holes and degrees of freedom in quantum gravity.
Martin Bojowald (Potsdam, Max Planck Inst.) . AEI-2005-115, Jun 2005. 4pp.
Published in Phys.Rev.Lett.95:061301,2005.
e-Print: gr-qc/0506128
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 27 times

5) Spherically symmetric quantum geometry: Hamiltonian constraint.
Martin Bojowald, Rafal Swiderski (Potsdam, Max Planck Inst.) . AEI-2005-171, NI05065, Nov 2005. 33pp.
Published in Class.Quant.Grav.23:2129-2154,2006.
e-Print: gr-qc/0511108
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 19 times

Some more here:

6) Wave functions for the Schwarschild black hole interior.
Daniel Cartin (Naval Acad. Prep. School, Newport) , Gaurav Khanna (Massachusetts U., North Dartmouth) . Feb 2006. 14pp.
Published in Phys.Rev.D73:104009,2006.
e-Print: gr-qc/0602025
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 5 times

9) Loop Quantum Dynamics of the Schwarzschild Interior.
Christian G. Boehmer (University Coll. London & Portsmouth U., ICG) , Kevin Vandersloot (Portsmouth U., ICG & Penn State U.) . Sep 2007. 15pp.
Published in Phys.Rev.D76:104030,2007.
e-Print: arXiv:0709.2129 [gr-qc]
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 5 times

10) Gravitational collapse in loop quantum gravity.
Leonardo Modesto (Bologna U. & INFN, Bologna) . Oct 2006. 16pp.
Published in Int.J.Theor.Phys.47:357-373,2008.
e-Print: gr-qc/0610074
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 4 times

Heavens! I don't know as I would recommend anyone to read these articles. Except what Shalayka said, maybe. The Gambini Pullin Campiglia one is recent and IIRC comparatively brief and clear. Jim I admire your energy and curiosity and I am very glad you plan to ask the appropriate people at the APS meeting.

Jim you asked was anything published about this? I listed that stuff just to show concretely a sample of what had been published. But I don't BELIEVE we humans have any very good notion of what happens down a black hole and all this work must necessarily be preliminary. The people doing it, if they are good, probably realize this better than anyone else.

What I believe is that geometry and matter are fundamentally the same and arise from the same basic microscopic D.O.F. stuff.
When it is very compressed, the distinction between matter and space disappears and one gets down to a stew of microscopic degrees of freedom, which we don't yet know how to model mathematically.

I believe it is the same kind of stuff that was there at bigbang time, at the beginning of expansion. That is, the stuff precedes classical cosmology. And the reason people call it FOAM is because by Heisenberg the geometry would have been very chaotic and unsmooth and hard to pin down.

The endpoint of something more and more complicated is something perfectly simple---call it foam, or Planck goo, or the Fire of Heracleitus. Or don't call it anything because we don't yet have a credible mathematical model so there is no convincing metaphor. It isn't "like" anything, yet.

that's just my attitude for the time being.

Heracleitus born c. 540 BC, Ephesus, in Anatolia [now Selçuk, Tur.] died c. 480

Greek philosopher remembered for his cosmology, in which fire forms the basic material principle of an orderly universe. Little is known about his life, and the one book he apparently wrote is lost. His views survive in the short fragments quoted and attributed to him by later authors.

Marcus is a bit biased towards one way of thinking (as I am, admittedly). You may find more interesting the following paper about the ``fuzzball'' paradigm proposed by Samir Mathur.

The picture solves many of the problems with traditional black hole physics, some of which are generically present in other approaches to quantum gravity.

One other point of view given recently is that of Christoph Schiller (the person responsible for the free physics textbook "Motion Mountain").

In the second paper of his series of four ("General relativity, gravitons and cosmology deduced from extended entities") he goes on to describe a method which logically removes black hole and universal (big bang) singularities.

Opinion may vary, and as far as I know, this work is not peer-reviewed yet. Even then, I found that it may be helpful to describe the thought patterns behind attempts at quantizing spacetime, and is also a good review of the more important tried-and-"true" equations related to General Relativity.

From what I can gather, Schiller's method may classify as a fuzzball.

P.S. I am naturally biased towards fuzzball methods mostly because I really love cats and they are generally cute little fuzzballs as well. Except for those hairless ones -- they're more like a naked singularity, I guess. :)

Quantum gravity singularity elimination talks.

I did hear Abhay’s and Gary’s talks yesterday. Basically, nothing was said that has not previously been published. Both agreed that singularities are probably eliminated by quantum gravity. Abhay talked mostly about cosmology, but said during the question period that similar things applied to black holes but the work was not as advanced and that the picture on the post collapse side still needed details worked out. But he said he was sure there was no singularity. Gary also said recent work favored no singularities, but he said he only had two strong arguments, not a proof. One argument, primarily due to Eva Siverstein, was perturbative and based on tachyon condensation smoothly pinching off the space before the singularity was reached. The other nonperturbative argument was based on Maldacena duality and concluded that a black hole could not exist because an infinite redshift event horizon could not exist without contradicting the Maldacena dual description. During the comment period Abhay said he doubted the second argument because it was too dependent on analyticity. He went on to say however that he also thought there was no event horizon, only an isolated horizon or a dynamic horizon. I had read or heard this before, but I thought this was only a mathematical technicality. However, Abhay seemed to think it was a necessary part of singularity elimination. I’ll probably post more later about the size of the “Planck goo”.
The key phrase is “Planck density”, not “Planck length.”
Bye for now. Best,
Jim Graber

I think the question basically is: Can intense radiation pressure be the support mechanism inside a black hole? I think it is logical that when a star above several solar masses collapses, the neutrons in the core disintegrate into radiation and some quark matter. As the collapse continues and temperature rises still further virtually all matter converts to radiation. If the radiation is contained in the system, the pressure of the radiation should be P = pc*2 , where p is the equivalent mass density of the radiation. The contained radiation, which has mass, basically acts like a compressed gas that can generate pressures exceeding neutron collapse pressure.

As I understand the TOV equation, dP/dr is proportional to p + P, which means if P is high enough there is runaway collapse. I don't think Einstein accepted this equation because he didn't believe in a point singularity.

That reminds me of a paper by Krasnov and Rovelli where they concluded that "for an observer at infinity" the black hole was described somewhat in that way. The Hilbert space of BH states was the space of intertwiners of some size determined by the area of the horizon. So a BH state (for an observer at infinity) would be an intertwiner.

But maybe there isn't yet one clear answer in the LQG context. I did a spires search on keywords "black hole and quantum gravity, loop space" and came up, for instance, with this:

Singularity Minded: The Black Hole Science that Won a Nobel Prize

The 2020 Nobel prize in physics has been jointly awarded to Roger Penrose, Reinhart Genzel, and Andrea Ghez for their contributions to our understanding of black holes — the Universe’s most mysterious and compact objects. Whilst Genzel and Ghez claim their share of the most celebrated prize in physics for the discovery of a supermassive compact object at the centre of our galaxy — an object that we would later come to realize was a supermassive black hole which was later named Sagittarius A* (Sgr A*) — Penrose is awarded his share for an arguably more fundamental breakthrough.

Sir Roger Penrose has been awarded the 2020 Nobel Prize in physics for his work revolutionising our theories regarding black holes and reshaping general relativity. (Robert Lea)

The Nobel is awarded to Penrose based on a 1965 paper in which he mathematically demonstrated that black holes arise as a direct consequence of the mathematics of Einstein’s theory of General Relativity. Not only this but for a body of a certain mass, the collapse into a singularity wasn’t just possible, or even probable. If that collapse could not be halted, singularity formation, Penrose argued, is inevitable.

“For the discovery, that black hole formation is a robust prediction of the general theory of relativity”

The Nobel Commitee awards the 2020 prize in physics to Sir Roger Penrose

The fact that Penrose showed that black holes mathematically emerge from general relativity may seem even more revolutionary when considering that the developer of general relativity — a geometric theory of gravity that suggests mass curves the fabric of spacetime — Albert Einstein did not even believe that black holes actually existed.

It was ten years after Einstein’s death in April 1955 when Penrose showed that singularities form as a result of the mathematics of general relativity and that these singularities act as the ‘heart’ of the black hole. At this central–or gravitational–singularity, Penrose argued, all laws of physics displayed in the outside Universe ceased to apply.

The paper published in January 1965 — just eight years after Penrose earned his Ph.D. from The University of Cambridge — ‘Gravitational Collapse and Spacetime Singularities’ is still widely regarded as the second most important contribution to general relativity after that of Einstein himself.

Yet, Penrose wasn’t the first physicist to mathematically unpick general relativity and discover a singularity. Despite this, his Penrose Singularity Theorem is still considered a watershed moment in the history of general relativity.

Black Holes: A Tale of Two Singularities

“A black hole is to be expected when a large massive body reaches a stage where internal pressure forces are insufficient to hold the body apart against the relentless inward pull of its own gravitational influence.”

Roger Penrose, The Road to Reality

Black holes are generally regarded as possessing two singularities a coordinate singularity and an ‘actual’ gravitational singularity. Penrose’s work concerned the actual singularity, so named because unlike the coordinate singularity, it could not be removed with a clever choice of coordinate measurement.

That doesn’t mean, however, that the coordinate singularity is unimportant or even easy to dismiss. In fact, you may already be very familiar with the coordinate singularity, albeit under a different name — the event horizon. This boundary marks the point where the region of space defined as a black hole begins, delineating the limit at which light can no longer escape.

The discovery of the event horizon occurred shortly after the first publication of Einstein’s theory of general relativity in 1915. In 1916, whilst serving on the Eastern Front in the First World War astrophysicist Karl Schwarzschild developed the Schwarzschild solution, which described the spacetime geometry of an empty region of space. One of the interesting features of this solution — a coordinate singularity.

The coordinate singularity — also often taking a third more official name as the Schwarzschild radius (Rs) — exists for all massive bodies at r =Rs = 2GM/c². This marks the point where the escape velocity of the body is such that not even light can escape its grasp. For most cosmic bodies the Schwarzschild radius falls well within its own radius (r). For example, the Sun’s Rs occurs at a radius of about 3km from the centre compared to an overall radius of 0.7 million km.

Thus, the Schwarzschild radius or event horizon marks the boundary of a light-trapping surface. A distant observer could see an event taking place at the edge of this surface, but should it pass beyond that boundary — no signal could ever reach our observer. An observer falling with the surface, though, would notice nothing about this boundary.

The passing of Rs would just seem a natural part of the fall to them despite it marking the point of no return. To the distant observer… the surface would freeze and become redder and redder thanks to the phenomena of gravitational redshift — also the reason the event horizon is sometimes referred to as the surface of infinite redshift.

The very definition of a black hole is a massive body whose surface shrinks so much during the gravitational collapse that its surface lies within this boundary. But, what if this collapse continues? When does it reach a central singularity at the heart of the black hole–r= 0 for the mathematically inclined?

Birthing a Black Hole

“We see that the matter continues to collapse inwards through the surface called the event horizon, where the escape velocity indeed becomes the speed of light. Thereafter, no further information from the star itself can reach any outside observer, and a black hole is formed.”

Roger Penrose, The Road to Reality

Penrose and other researchers have found that the equations of general relativity open the possibility that a body may undergo a complete gravitational collapse — shrinking to a point of almost infinite density — and become a black hole.

In order for this to happen, however, a series of limits have to be reached and exceeded. For example, planets are unable to undergo this gravitational collapse as the mass they possess is insufficient to overcome the electromagnetic repulsion between their consistent atoms — thus granting them stability.

Likewise, average-sized stars such as the Sun should also be resistant to gravitational collapse. The plasma found at the centre of stars in this solar-mass range is believed to be roughly ten times the density of lead protecting from complete collapse, whilst the thermal pressure arising from nuclear processes and radiation pressure alone would be sufficient to guarantee a star of low to intermediate-mass stability.

For older, more evolved stars in which nuclear reactions have ceased due to a lack of fuel. It’s a different story. Especially if they have a mass ten times greater than the Sun.

It was suggested as early as the 1920s that small, dense stars — white dwarf stars — were supported against collapse by phenomena arising from quantum mechanics called degeneracy.

This ‘degeneracy pressure’ arises from the Pauli exclusion principle, which states that fermions such as electrons are forbidden from occupying the same ‘quantum state’. This led a physicist called Subrahmanyan Chandrasekhar to question if there was an upper limit to this protection.

In 1931, Chandrasekhar proposed that above 1.4 times the mass of the Sun, a white dwarf would no longer be protected from gravitational collapse by degeneracy pressure. Beyond this boundary— unsurprisingly termed the Chandrasekhar limit — gravity overwhelms the Pauli exclusion principle and gravitational collapse continues unabated.

Cross Section of A Black Hole (©Johan Jarnestad/The Royal Swedish Academy of Sciences)

The discovery of neutrons — the neutral partner of protons in atomic nuclei — in 1932 led Russian theorist Lev Landau to speculate about the possibility of neutron stars. The outer part of these stars would contain neutron-rich nuclei, whilst the inner sections would be formed from a ‘quantum-fluid’ comprised of mostly neutrons.

Again, neutron stars would be protected against gravitational collapse by degeneracy pressure — this time provided by this neutron fluid. In addition to this, the greater mass of the neutron in comparison to the electron would allow neutron stars to reach a greater density before undergoing collapse.

To put this into perspective, a white dwarf with the mass of the Sun would be expected to have a millionth of our star’s volume — giving it a radius of
5000 km roughly that of the Earth. A neutron star of a similar mass though, that would have a radius of about 20km — roughly the size of a city.

By 1939, Robert Oppenheimer had calculated that the mass-limit for neutron stars would be roughly 3 times the mass of the Sun. Above that limit — again, gravitational collapse wins. Oppenheimer also used general relativity to describe how this collapse appears to a distant observer. They would consider the collapse to take an infinitely long time, the process appearing to slow and freeze as the star’s surface shrinks towards the Schwarzschild radius.

Straight to the Heart: The Inevitability of the cental singularity

“So long as Einstein’s picture of classical spacetime can be maintained, acting in accordance with Einstein’s equation then a singularity will be encountered within a black hole. The expectation is that Einstein’s equation will tell us that this singularity cannot be avoided by any matter in the hole…”

Roger Penrose, The Road to Reality

For Penrose, the mathematical proof of a physical singularity at the heart of a black hole arising from this complete collapse was not enough. He wanted to demonstrate the singularity and the effects on a spacetime that would arise there. He did so with the use of ‘light cones’ travelling down a geodesic — an unerringly straight line. In the process, he unveiled the anatomy of the black hole.

Lightcones: A Physicist’s Favorite Tool (Robert Lea)

A light cone is most simply described as the path that a flash of light created by a single event and travelling in all directions would take through spacetime. Light cones can be especially useful when it comes to physicists calculating which events can be causally linked. If a line can’t be drawn between the two events that fits in the light cone, one cannot have caused the other.

We call a line emerging from a lightcone a ‘world-line’–these move from the central event out through the top of the cone–the future part of the diagram. The worldline shows the possible path of a particle or signal created by the event at the origin of the lightcone. Throwing a light cone at a black hole demonstrates why passing the event horizon means a merger with the central singularity is inevitable.

Penrose considered what would happen to a light cone as it approached and passed the event horizon of what is known as a ‘Kerr black hole.’ This is a black hole that is non-charged and rotating. Its angular momentum drags spacetime along with it in an effect researchers call frame dragging.

Far from the black hole, light is free to travel with equal ease in any direction. The lightcones here have a traditionally symmetrical appearance which represents this.

Using Lightcones to Probe Black Holes ((©Johan Jarnestad/The Royal Swedish Academy of Sciences))

However, towards the static limit — the point at which the black hole starts to drag spacetime around with it — the lightcones begin to tip towards the singularity and in the direction of rotation and narrow. Thus the static limit represents the point at which light is no longer free to travel in any direction. It must move in a direction that doesn’t oppose the rotation of the black hole. Particles at this limit can no longer sit still — hence the name static limit.

Yet, despite the fact the dragging effect is so strong, here that not even light can resist it, signals can escape this region — it isn’t the event horizon — but they can only do so by travelling in the direction of the rotation.

Interestingly, Penrose suggests that particles entering the static limit and decaying to two separate particles may result in energy leaching from the black hole in what is known as the Penrose process, but that’s a discussion for another time.

Probing Black Holes with Lightcones (Robert Lambourne/ Robert Lea)

So as our light cone moves toward the event horizon, it begins to narrow and tip. But, something extraordinary happens when it passes this boundary. As long as one is using so-called Swartzchild coordinates, once ‘inside the black hole’ proper, the lightcone flips on its side, with the ‘future end’ of the cone pointed towards the singularity.

This can mean only one thing for the worldline of that event, it points to the central singularity signalling that an encounter with that singularity is evitable.

The Anatomy of a Black Hole

“It is generally believed that the spacetime singularities of gravitational collapse will necessarily always lie within an event horizon, to that whatever happens to be the extraordinary physical effects at such a singularity, these will be hidden from the view of any external observer.”

Roger Penrose, The Road to Reality

Black holes aren’t particularly complex in construction and posses only three properties –mass, electric charge, and angular momentum–but physicists working with light cones were able to determine the layers of their anatomy–and crucially, the bounded surfaces that exist within them.
This is what was revolutionary about Penrose’s concepts, they introduced the concept of bounded surfaces to black holes.

The structure of a Kerr (rotating) Black Hole. (Robert Lambourne/ Robert Lea)

Looking back on this from an era in which a black hole has been imaged for the first time and gravitational waves are beginning to be routinely measured from the mergers of such objects, it’s important to not underestimate the importance of Penrose’s findings.

Before any practical developments surround black holes could even be dreamed of, Roger Penrose provided the mathematical basis to not just suggest the existence of black holes, but also laying the groundwork for their anatomy, and the effect they have on their immediate environment.

Thus, what Penrose’s Nobel award can really be seen as a recognition of moving these objects — or more accurately, spacetime events — from the realm of speculation to scientific theory.

The first-ever image of a black hole was released 2019 came decades after Roger Penrose demonstrated such spacetime events are inevitable in the ungoverned collapse of a star with enough mass. (Event Horizon Telescope collaboration et al)

Original research and further reading

Penrose. R., ‘Gravitational Collapse and Space-Time Singularities,’ Physical Review Letters, vol. 14, Issue 3, pp. 57-59, [1965]

Penrose. R., ‘The Road to Reality,’ Random House, 2004

Senovilla. J. M. M., Garfinkle. G., ‘The 1965 Penrose Singularity Theorem,’ Classical and Quantum Gravity, [2015].

Relativity, Gravitation and Cosmology, Robert J. Lambourne, Cambridge Press, 2010.

Relativity, Gravitation and Cosmology: A basic introduction, Ta-Pei Cheng, Oxford University Press, 2005.

Extreme Environment Astrophysics, Ulrich Kolb, Cambridge Press, 2010.

Stellar Evolution and Nucleosynthesis, Sean G. Ryan, Andrew J. Norton, Cambridge Press, 2010.

Black holes and the singularity

I don't think there's a "mainstream" answer to this current physics simply breaks down at a singularity. Mainstream science can say what a black hole does, but not what it is, and given that mainstream science also expects a singularity to be behind an event horizon, there is no way to distinguish between alternative ideas.

I do not consider it proven yet that black holes actually occur. There is certainly solid observational evidence that extremely massive but compact objects exist which must be black holes if General Relativity remains accurate even in such extreme cases. The first LIGO detection also confirmed that the physical sizes of such objects must be close to the predictions for black holes of a few stellar masses. However, some of those objects behave in ways which are difficult to reconcile with the GR predictions of black holes, for example apparently having intense magnetic fields or having X-ray luminosity which appears to far exceed the theoretical maximum from current black hole models.

If these objects aren't in fact black holes, then one way to tell would be that a collision between them would give off a significant amount of electromagnetic radiation as well as gravitational radiation, so when the Fermi Gamma-Ray Space Telescope team claimed an apparent observation of a gamma-ray burst (close to the limit of detectability) associated with the first LIGO detection I found that very interesting, although that result was controversial and marginal. I hope that LIGO will get some more strong results soon to allow further checking for possible correlated GRBs.