# How can a naked singularity be possible?

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How can we have a singularity, without a black hole around it? How would one form? What does it do?

Nobody likes the idea of naked singularities, as they would have a toxic effect on causality. If a singularity existed that was not separated from us by an event horizon, then not only would the future not be predictable, but the past would not be fixed. Like the grandfather paradox, it wouldn't make sense, so it cant exist. The trouble is that GR doesn't implicitly rule them out.

If a black hole is spinning fast enough, or has enough charge then it seems a naked singularity could form. Naively you may think that the centrifugal force in the first case, and the electromagnetic force in the second are sufficient to overcome gravity.

I particular if $G^2M^4/c^2 < J^2$, where J is angular momentum, M is the mass, G is the gravitation constant, and c is the speed of light. The there will be a naked singularity. For a small, stellar mass black hole would need an angular momentum of $10^{42} mathrm{kg m^2 s^{-1}}$ to lose its event horizon

## Naked Singularity, Black hole mass limit

I came across a question on PSE. I am not sure its a violation to ask the same question here, but theres no answer to the question in there so I wanted to ask it here.

"Since the universe has a positive cosmological constant, there is an upper limit on the mass of the black holes as evident from the so-called Schwarzschild-de Sitter metric:

$ds^2 = -f(r)dt^2 + dfrac<1> dr^2 + r^2 dOmega_2^2$

It suggests that a singularity would be a black hole only if the mass is not greater than ##dfrac<1><3sqrt>## and if the mass exceeds this limit then the singularity would become naked. But if we consider the Cosmic Censorship seriously then we must expect that (since the naked singularities can't exist) no singularity can have a mass greater than ##dfrac<1><3sqrt>##. This suggests that there is an upper limit on mass itself (namely, ##dfrac<1><3sqrt>##) that can be put inside a radius of ##dfrac<2><3sqrt>##. Thus, within a radius ##R##, mass can't ever exceed ##dfrac<1><3sqrt>## if ##Rleqdfrac<2><3sqrt>##. (Perhaps, by perpetually shifting the origin of the coordinate set-up to cover the desired region, I can argue that within a radius ##R##, mass can't exceed ##dfrac<3sqrt>## if ##n## is the smallest possible integer solution for ##l## where ##Rleqdfrac<2l><3sqrt>##.) If we consider censorship seriously, then it doesn't suggest that if the mass exceeds this limit then it will form a naked singularity but it rather suggests that mass just can't exceed this limit.

This seems result seems quite interesting to me and I can't figure out as to what reason or mechanism would keep the mass from crossing this limit. What is the resolution to this question (provided it demands a resolution)?"

## What would a naked singularity look like ?

I've been documenting myself a bit about naked singularities lately and I'm wondering, what would one look like ? How would it affect the outside world ? For those of you who don't know, naked singularities are basically theoretical black holes without an event horizon, so you would be able to see the singularity inside directly.
To come back to my question, since they have no gravitational pull (I'm only guessing here, but since they don't have an event horizon I assume they have no gravitational pull either) they wouldn't have much of an effect on their neighbourhood, neither through gravitational interactions nor EM pulses since AFAIK these are generated when matter falls into a black hole, which wouldn't happen here.
What would we see then ? How could we detect one ?

To come back to my question, since they have no gravitational pull

This is not true. The curvature of spacetime is still non-trivial near a naked singularity, and so there is certainly gravity. A superextremal Kerr black hole, for instance, functions just like any other mass from a sufficient distance. Objects can orbit the singularity just fine.

For those of you who don't know, naked singularities are basically theoretical black holes without an event horizon, so you would be able to see the singularity inside directly.

A naked singularity is simply a gravitational singularity not enclosed within an event horizon. So the big bang singularity is, in fact, a naked singularity. The singularity of a super-extremal Kerr black hole is also a naked singularity. In principle, you could travel arbitrarily close to the singularity and then come back. (For a super-extremal charged black hole, the singularity is actually repulsive at sufficiently small distances, independent of the sign of the electric charge. No free-falling particle can actually ever reach the naked singularity in such a black hole. To get arbitrarily close, you would have to have a rocket and actually apply some non-zero thrust.)

The singularity is still, well, a singularity. So paths that lead into the singularity cannot necessarily be extended beyond the singularity. This presents some problems regarding whether these singularities can exist in nature. For one, this means that it would be possible to observe a star or other massive object collapse into an object of infinite density (and this can actually be witnessed since the singularity is not beyond an event horizon). Of course, all current theories of gravitational collapse would leave the singularity hidden behind an event horizon. So it's not clear how a naked singularity, other than the big bang, could ever occur naturally.

A naked singularity should probably be completely black as well. Just as null geodesics leading into the singularity cannot be extended, there's no meaningful notion of null geodesics leading out of the singularity. So the singularity should not emit any light of any kind.

Currently we don't know whether naked singularities could even exist. Right now we don't know of any mechanism that could lead to their existence, and other than the big bang, we don't know of any that actually do exist. (This is captured in the cosmic censorship hypothesis, which proposes that all singularities, other than the big bang, must be enclosed by an event horizon.) The cosmic censorship hypothesis is not a proven fact though, it is just a hypothesis. It may well be the case that quantum gravity shows naked singularities to be a real thing.

## Naked Singularities Can Form in ‘Saddle-Shaped’ Universe, Physicists Say

A team of theoretical physicists at the University of Cambridge, UK, has used computer simulations to predict the existence of a so-called naked singularity, which interferes with Albert Einstein’s general theory of relativity.

A simulated black hole of 10 solar masses as seen from a distance of 370 miles. Image credit: Ute Kraus, Universität Hildesheim / Axel Mellinger / CC BY-SA 2.5.

Einstein’s general theory of relativity underpins our current understanding of gravity: everything from the estimation of the age of the stars in the Universe, to the GPS signals we rely on to help us navigate, is based on his equations.

In part, the theory tells us that matter warps its surrounding space-time, and what we call gravity is the effect of that warp.

In the 100 years since it was published, general relativity has passed every test that has been thrown at it, but one of its limitations is the existence of singularities — points where gravity is so intense that space, time, and the laws of physics, break down.

General relativity predicts that singularities exist at the center of black holes, and that they are surrounded by an event horizon — the ‘point of no return’, where the gravitational pull becomes so strong that escape is impossible, meaning that they cannot be observed from the outside.

For more than four decades, theoretical physicists have proposed that whenever singularities form, they will always be hidden from view in this way — this is known as the ‘cosmic censorship conjecture.’

If true, cosmic censorship means that outside of black holes, these singularities have no measurable effect on anything, and the predictions of general relativity remain valid.

In recent years, scientists have used computer simulations to predict the existence of ‘naked singularities’ — that is, singularities which exist outside an event horizon.

Naked singularities would invalidate the cosmic censorship conjecture and, by extension, general relativity’s ability to explain the Universe as a standalone theory.

However, all of these predictions have been modeled on universes which exist in higher dimensions.

For example, in 2016, researchers from the University of Cambridge and Queen Mary University of London predicted the existence of a naked singularity, but their predictions were based on a 5D Universe.

The new research, published in the journal Physical Review Letters, has predicted the existence of a naked singularity in a 4D Universe — three spatial dimensions, plus time — for the first time.

The predictions show that a naked singularity can form in a special kind of curved space known as anti-de Sitter space, in which the Universe has a distinctive ‘saddle’ shape.

According to general relativity, universes can have various shapes, and anti-de Sitter space is one of these possible shapes.

Anti-de Sitter space has a very different structure to flat space. In particular it has a boundary which light can reach, at which point it is reflected back.

“It’s a bit like having a space-time in a box,” said first author Toby Crisford, from the University of Cambridge’s Department of Applied Mathematics and Theoretical Physics.

“At the boundary, the walls of the box, we have the freedom to specify what the various fields are doing, and we use this freedom to add energy to the system and eventually force the formation of a singularity.”

While the results are not directly applicable to our Universe, as ‘forcing’ a singularity is not a procedure which is possible to simulate in flat space, they do open up new opportunities to study other theories to understand the Universe.

One such theory could involve quantum gravity, which provides new equations close to a singularity.

“The naked singularity we see is likely to disappear if we were to include charged particles in our simulation — this is something we are currently investigating,” said co-author Dr. Jorge Santos, also from the University of Cambridge’s Department of Applied Mathematics and Theoretical Physics.

“If true, it could imply a connection between the cosmic censorship conjecture and the weak gravity conjecture, which says that any consistent theory of quantum gravity must contain sufficiently charged particles.”

“In anti-de Sitter space, the cosmic censorship conjecture might be saved by the weak gravity conjecture.”

Toby Crisford & Jorge E. Santos. 2017. Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space. Phys. Rev. Lett. 118 (18): 181101 doi: 10.1103/PhysRevLett.118.181101

## Naked Singularities Can Actually Exist in a Three-Dimensional Universe, Physicists Predict

For the first time, physicists have demonstrated that a universe like ours with three spatial dimensions could actually host a naked singularity - an event so intense, the laws of physics would fall apart.

Until now, researchers have only been able to place naked singularities in five-dimensional universes, but by proving that they could theoretically exist in three spatial dimensions, these physicists have found something that could challenge Einstein's general theory of relativity.

If you're not familiar with naked singularities, think of them like a black hole that's been turned inside-out - if you could take all the strangeness that's inside a black hole, and expose it to the Universe as a naked entity, that's what we're talking about here.

No one's ever detected a naked singularity in our Universe, but these hypothetical regions in space are predicted to form when huge stars collapse at the end of their lives, resulting in literally infinite density - something that our laws of physics cannot handle.

That means if a black hole's unimaginably violent centre could potentially occur in open space, someone's going to have to explain why general relativity - something that's supposed to be universal - no longer applies.

"A naked singularity, if such a thing exists, would be an abrupt hole in the fabric of reality - one that would not just distort space-time, but would also wreak havoc on the laws of physics wherever it goes and lead to a catastrophic loss of predictability," Avaneesh Pandey from the International Business Times explains.

For decades, physicists thought that black holes and their mysterious internal singularities could exist in harmony with Einstein's general relativity due to something called the 'cosmic censorship conjecture.'

The basic idea is that whenever a singularity forms in the Universe, it will always be hidden away behind a black hole's event horizon, which means the laws of physics around the black hole can continue to function as normal.

"If true, cosmic censorship means that outside of black holes, these singularities have no measurable effect on anything, and the predictions of general relativity remain valid," Sarah Collins writes for Phys.org.

More recently, mathematical simulations of five-dimensional universes have predicted the existence of naked singularities that would throw the idea of cosmic censorship conjecture out the window.

That's not so bad - we've never even come close to finding another universe, especially one with five dimensions, so general relativity can go on its merry way.

Except that now UK physicists Toby Crisford and Jorge Santos from the University of Cambridge have simulated a universe with the same number of dimensions as our own, and lo and behold - it can host naked singularities too.

To be clear, the pair aren't saying they've simulated a naked singularity in our Universe per se - the universe they've simulated has three spatial dimensions and one time dimension like ours, but it's got a whole different shape.

While our Universe is thought to be fairly flat, Crisford and Santos's universe is 'saddle-shaped'.

General relativity allows for the existence of many differently shaped universes, and the pair worked with a specific type of curved universe called Anti-de Sitter space, as seen below:

One particular feature of this saddle-shaped universe is a point of no return, where light is actually reflected back onto itself.

It's a bit like putting space-time in a box, and at the walls of this box, the physicists were able to force the formation of a singularity.

So what does this mean for us?

Well, the good news is that no one's been able to prove that naked singularities exist in our Universe, which is just as well, because black holes are bad enough company as it is - space-time in a box as it is - imagine those cataclysmic death traps without an event horizon.

But by demonstrating that naked singularities are actually possible in a universe like ours with three spatial dimensions, Crisford and Santos have a promising new set-up for us to find quantum gravity - something that could one day merge general relativity with quantum mechanics as a universal 'theory of everything'.

"The naked singularity we see is likely to disappear if we were to include charged particles in our simulation - this is something we are currently investigating," Santos told Phys.org.

"If true, it could imply a connection between the cosmic censorship conjecture and the weak gravity conjecture, which says that any consistent theory of quantum gravity must contain sufficiently charged particles. In Anti-de Sitter space, the cosmic censorship conjecture might be saved by the weak gravity conjecture."

It's heady stuff, but if the strangeness of naked singularities can help us finally fill the gaps in modern physics, we're glad they exist (in theory).

## Singularity

Singularities occur at the center of black holes. Because the General Theory of Relativity is a theory of space-time as well as of gravity, the consequences of the unbounded energy densities predicted by that theory at the end of gravitational collapse and at the start of the universe are catastrophic, for they imply an end to space-time itself. The possible history of an observer or particle simply comes to an end physics breaks down, and space-time ceases to exist. It is difficult even to begin talking about this situation, for even the word exist ceases to have meaning. It is unclear if quantum gravity theories will avoid this implication.

An unresolved problem pertaining to singularities is whether gravitational collapse can lead to a naked singularity, that is, one that will be visible from far away and so can influence events in the outside world. The contrary of this possibility is that a naked singularity can only lead to a black hole, where a singularity occurs but is hidden from the outside world by an event horizon.

See also Black Hole Cosmology, Physical Aspects Gravitation Relativity, General Theory of Space and Time

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## Genealogy of the (Maybe Impossible) Naked Singularity

Many of you responded to yesterday's item about the work on naked singularities, arguing that in fact the team hadn't done anything new. I think that's partially my fault in not giving some more background, and since it's interesting stuff, here goes:

A black hole itself is typically created, physicists believe, when an object such as a star collapses in on itself. Its gravitational force twists space around it (as expressed in Einstein's theory of general relativity) so strongly that ultimately, light itself can't escape. The radius at which regular laws of physics break down is called the event horizon. Because nothing can pass out of this zone, there seems to be no way that scientists can observe the black hole, or singularity, that exists beyond this point, a phenomenon that's been dubbed the “cosmic censorship hypothesis.”

By the early 1990s, some physicists had suggested the notion of a
“naked” singularity, or one that did not have this event horizon, and might thus be observable from the outside. The idea was controversial enough to disgust Cambridge's Stephen Hawking, who in 1991 bet two proponents of the theory \$100 and a T-shirt that no such phenomenon was possible.

It took six years for the bet to be concluded. A University of Texas supercomputer analysis showed that under specific conditions, a naked singularity could be formed. On the strength of this, Hawking reluctantly paid up, with the bet's bounty including T-shirts reading
“Nature Abhors a Naked Singularity.”

But perhaps fittingly for the mysteries of a black hole, other physicists argued that Hawking shouldn't have paid, because even though the naked singularity could exist, the probability of it forming was mathematically zero.

For more on the bet, a 1997 New York Times article outlines the story well here. And a Princeton professor's response on the zero-probability issue is here.

The new work from the Duke/Cambridge team, which I wrote about yesterday, could add new grist to that debate. Their argument is that a singularity could in effect shed its impenetrable event horizon under some conditions, and become directly observable through the phenomenon of gravitational lensing (in which a dense object bends space enough to split the light from background objects into multiple images).

However, I'm not at all qualified to critique the math -- the more detail-minded among you should certainly check out the full article in Physical Review D.

(Image: Artist's conception of a supermassive black hole -- not a naked one -- at the center of a galaxy. Credit: NASA/JPL-Caltech)

## Contents

The singularities discussed in this article are also called true, intrinsic, or curvature singularities, to indicate that they are physical properties of spacetime. In them a coordinate-independent quantity diverges, the curvature of spacetime. They are to be distinguished from so-called coordinate singularities , which are merely a mathematical property of the selected coordinates. The latter can be "transformed away" by means of a suitable coordinate transformation . This is not possible for real , essential singularities , here a new theory (a new physical law) is needed.

Singularities, for example within a normal black hole , are surrounded by an event horizon , which in principle withdraws the object from observation. It is unclear whether singularities without an event horizon (so-called naked singularities ) also exist. That singularities are shielded by event horizons, i.e. there are no naked singularities, is the subject of the hypothesis of the cosmic censor by Roger Penrose . It is unproven and represents one of the great open problems of general relativity.

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Research output : Contribution to journal › Article › peer-review

T1 - Naked singularities as particle accelerators. II

N2 - We generalize here our earlier results on particle acceleration by naked singularities. We showed recently that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as the final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.

AB - We generalize here our earlier results on particle acceleration by naked singularities. We showed recently that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as the final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.

## Making a difference

A theoretical physicist took this challenge head-on by studying if a naked singularity could reveal itself in other ways, especially if it's surrounded by a ring of material, as reported in a paper published Nov. 12 on the preprint journal server arXiv. This ring, called an accretion disk, is a common feature around black holes (and potentially naked singularities). When gas and dust fall onto a dense, compact object, that material flattens into a disk before funneling all the way down. This disk can be incredibly bright, betraying the existence of a black hole (in fact, this is how we know of the existence of the vast majority of the black holes in the universe).

Most theoretical studies of naked singularities have assumed that the object exists in isolation, which isn't true in the real universe. In the new work, the theorist examined the whole, complex situation, and found a surprising result.

The accretion disk is not completely separate from the black hole (or naked singularity). The disk itself has its own gravitational pull, and it can twist and distort the compact object at the center. This distortion in turn affects the gravitational environment around the object, subtly altering the path of the material swirling inward.

The theorist found that a naked singularity does behave a little bit differently than a normal black hole –- the accretion disk around a naked singularity can be much, much brighter than around a black hole. So far our telescopes don't have the sensitivity to tell the difference, future instruments could perhaps an updated version of the Event Horizon Telescope would do the trick.

Finding a naked singularity out in the wild would be a major revelation in physics. We would be able to point to a location on the sky where we know that our knowledge breaks down. More detailed studies of the environment around a confirmed naked singularity would divulge some of the deepest mysteries of the universe.