Where is the singularity found in a black hole

Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected. Moderators are staffed during regular business hours New York time and can only accept comments written in English. We care about your data, and we'd like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy. Read Later. For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.

James Zanoni. The Quanta Newsletter Get highlights of the most important news delivered to your email inbox. They only ever materialized cloaked inside a black hole. Penrose pieced together clues that suggested a conjecture—an informed guess, not an airtight proof—that general relativity would never make that prediction. Cosmic censorship is an idea that sounds to physicists like it must be right, and most assume it is.

Although researchers have suggested ways to spot naked singularities —observable signs that could distinguish them from black holes—astronomers have not yet seen any evidence of them. Then, in , physicists Luis Lehner and Frans Pretorius used a computer simulation to show that the outer surface of black holes could break into pieces and leave behind naked singularities.

The fracturing comes with a curious twist, though. It happens through a process, the so-called Gregory-Laflamme instability , that can only happen in universes with more than three dimensions of space.

Despite this caveat, the result still has meaning. According to Figueras, the field has gained momentum in the past decade, thanks largely to advances in computing that have made it possible to calculate how black holes evolve and, in some cases, fall apart to reveal singularities.

Figueras and his colleagues have demonstrated, for instance, that naked singularities can show up when black holes collide. Such collisions happen even in our university. The dynamics of those cosmological models is largely governed by the behavior of the cosmological expansion factor, a measure of the relative sizes of local regions of space not spacetime at different cosmological times.

If the universe's expansion stops, and the net gravitational effect on cosmological scales results in the universe's collapsing in on itself, this would be marked by a continual decrease in the expansion factor, eventuating in a Big Crunch singularity as the expansion factor asymptotically approached zero.

The remaining dynamics of these cosmological models is encoded in the behavior of the Hubble parameter, a natural measure of the rate of change of the expansion factor. A sudden singularity, then, is defined by the divergence of a time derivative of the expansion factor or the Hubble parameter, though the factor or parameter itself remains finite.

In such cases, it may happen that the mass-density of the fluid itself, the expansion factor and its first derivative, and even the Hubble parameter and its first derivative, all remain finite: only the pressure and so the second derivative of the expansion factor diverges. Because the physical significance of quantities such as pressure is thought to be unambiguous, this feature of sudden singularities stands in marked contrast to the problems of physical interpretation that plague the standard type of singularity, discussed in section 1.

Indeed, point particles passing through the sudden singularity would not even notice the pathology, as only tidal forces may diverge and not even all sudden singularities involve divergence of those : point particles, having no extension, cannot experience tidal force. Although the discovery of sudden singularities has reinvigorated the study of singular spacetimes in the physics community Cotsakis , they remain so far almost entirely unexamined by the philosophy community.

Nonetheless, they raise questions of manifest philosophical interest and import. The fact that they are such radically different structures from all other previously known kinds of singularity, for example, raises methodological questions about how to understand the meaning of terms in physical theories when those terms refer to structurally quite different but obviously still intimately related phenomena—the reasons for thinking of them as singularities are compelling, even though they violate essentially every standard condition known for characterizing singularities.

Another unusual kind of singularity characterized only recently characterized deserves mention here, because of its possible importance in cosmology.

The physical processes that seem to eventuate in most known kinds of singular structure involve the unlimited clumping together of matter, as in collapse singularities associated with black holes, and the Big Bang and Big Crunch singularities of standard cosmological models.

A big rip , contrarily, occurs when the expansion of matter increasingly accelerates without bound in a finite amount of proper time Caldwell ; Caldwell et al. Again, standard concepts and arguments about singularities characterized as incomplete paths do not seem easily applicable here. Although big rips do have incomplete paths associated with them as well as curvature pathology, they are of such radically different kinds as to prima facie warrant separate analysis.

Recent work, codified by Harada et al. For homogeneous cosmological models filled with perfect fluids with a linear equation of state—the standard cosmological model—certain values of the barotropic index yield past, future, or past and future big rips that are such that every timelike geodesic runs into them, but every null geodesic avoids them. See note 7 for an explanation of the barotropic index.

In other words, any body traveling more slowly than light will run into the singularity, but every light ray will escape to infinity. This is not a situation that lends itself to easy and perspicuous physical interpretation.

When considering the implications of spacetime singularities, it is important to note that we have good reasons to believe that the spacetime of our universe is singular.

In the late s, Penrose, Geroch, and Hawking proved several singularity theorems, using path incompleteness as a criterion Penrose , ; Hawking , b, c, d; Geroch , , b, ; Hawking and Penrose These theorems showed that if certain physically reasonable premises were satisfied, then in certain circumstances singularities could not be avoided. Notable among these conditions is the positive energy condition, which captures the idea that energy is never negative. These theorems indicate that our universe began with an initial singularity, the Big Bang, approximately 14 billion years ago.

They also indicate that in certain circumstances discussed below collapsing matter will form a black hole with a central singularity. According to our best current cosmological theories, moreover, two of the likeliest scenarios for the end of the universe is either a global collapse of everything into a Big Crunch singularity, or the complete and utter diremption of everything, down to the smallest fundamental particles, in a Big Rip singularity.

See Joshi for a recent survey of singularities in general, and Berger for a recent survey of the different kinds of singularities that can occur in cosmological models. Should these results lead us to believe that singularities are real? Many physicists and philosophers resist this conclusion. Some argue that singularities are too repugnant to be real. Others argue that the singular behavior at the center of black holes and at the beginning and possibly the end of time indicates the limit of the domain of applicability of general relativity.

Some are inclined to take general relativity at its word, however, and simply accept its prediction of singularities as a surprising but perfectly consistent account of the possible features of the geometry of our world. See Curiel and Earman , for discussion and comparison of these opposing points of view.

In this section, we review these and related problems and the possible responses to them. Let us summarize the results of section 1 : there is no commonly accepted, strict definition of singularity; there is no physically reasonable characterization of missing points; there is no necessary connection between singular structure, at least as characterized by the presence of incomplete paths, and the presence of curvature pathology; and there is no necessary connection between other kinds of physical pathology such as divergence of pressure and path incompleteness.

What conclusions should be drawn from this state of affairs? There seem to be two basic kinds of response, illustrated by the views of of Clarke and Earman on the one hand, and those of Geroch et al.

The former holds that the mettle of physics and philosophy demands that we find a precise, rigorous and univocal definition of singularity.

On this view, the host of philosophical and physical questions surrounding general relativity's prediction of singular structure would best be addressed with such a definition in hand, so as better to frame and answer these questions with precision, and thus perhaps find other, even better questions to pose and attempt to answer. The latter view is perhaps best summarized by a remark of Geroch et al.

In sum, the question becomes the following: is there a need for a single, blanket definition of singularity or does the urge for one betray only an old Aristotelian, essentialist prejudice? This question has obvious connections to the broader question of natural kinds in science. One sees debates similar to those canvassed above when one tries to find, for example, a strict definition of biological species. Clearly, part of the motivation for searching for a single exceptionless definition is the impression that there is some real feature of the world or at least of our spacetime models that we can hope to capture precisely.

Further, we might hope that our attempts to find a rigorous and exceptionless definition will help us to better understand the feature itself. Even without an accepted, strict definition of singularity for relativistic spacetimes, the question can be posed: what would it mean to ascribe existence to singular structure under any of the available open possibilities? It is not far-fetched to think that answers to this question may bear on the larger question of the existence of spacetime points in general Curiel , ; Lam See the entries The Hole Argument and Absolute and Relational Theories of Space and Motion for discussions of the question of the existence of spacetime itself.

It would be difficult to argue that an incomplete path in a maximal relativistic spacetime does not exist in at least some sense of the term. It is not hard to convince oneself, however, that the incompleteness of the path does not exist at any particular point of the spacetime in the same way, say, as this glass of beer exists at this point of spacetime. If there were a point on the manifold where the incompleteness of the path could be localized, surely that would be the point at which the incomplete path terminated.

But if there were such a point, then the path could be extended by having it pass through that point. It is perhaps this fact that lies behind much of the urgency surrounding the attempt to define singular structure as missing points. Aristotelian substantivalism here refers to the idea contained in Aristotle's contention that everything that exists is a substance and that all substances can be qualified by the Aristotelian categories, two of which are location in time and location in space.

Such a criterion, however, may be inappropriate for features and properties of spacetime itself. Several essential features of a relativistic spacetime, singular or not, cannot be localized in the way that an Aristotelian substantivalist would demand.

For example, the Euclidean or non-Euclidean nature of a space is not something with a precise location. See Butterfield for discussion of these issues. Likewise, various spacetime geometrical structures such as the metric, the affine structure, the topology, etc. Because of the way the issue of singular structure in relativistic spacetimes ramifies into almost every major open question in relativistic physics today, both physical and philosophical, it provides a peculiarly rich and attractive focus for these sorts of questions.

An interesting point of comparison, in this regard, would be the nature of singularities in other theories of gravity besides general relativity. Weatherall's characterization of singularities in geometrized Newtonian gravitational theory, therefore, and his proof that the theory accommodates their prediction, may serve as a possible testing ground for ideas and arguments on these issues. General relativity admits spacetimes exhibiting a vast and variegated menagerie of structures and behaviors, even over and above singularities, that most physicists and philosophers would consider, in some sense or other, not reasonable possibilities for physical manifestation in the actual world.

Manchak has argued that there cannot be purely empirical grounds for ruling out the seemingly unpalatable structures, for there always exist spacetimes that are, in a precise sense, observationally indistinguishable from our own Malament ; Manchak a that have essentially any set of properties one may stipulate. Norton argues that this constitutes a necessary failure of inductive reasoning in cosmology, no matter what one's account of induction.

Butterfield discusses the relation of Manchak's results to standard philosophical arguments about under-determination of theory by data. The philosopher of science interested in the definition and status of theoretical terms in scientific theories has at hand here a rich possible case-study, enlivened by the opportunity to watch eminent scientists engaged in fierce, ongoing debate over the definition of a term—indeed, over the feasibility of and even need for defining it—that lies at the center of attempts to unify our most fundamental physical theories, general relativity and quantum field theory.

At the heart of all of our conceptions of a spacetime singularity is the notion of some sort of failure: a path that disappears, points that are torn out, spacetime curvature or some other physical quantity such as pressure whose behavior becomes pathological. Perhaps the failure, though, lies not in the spacetime of the actual world or of any physically possible world , but rather in our theoretical description of the spacetime. That is, perhaps we should not think that general relativity is accurately describing the world when it posits singular structure—it is the theory that breaks down, not the physical structure of the world.

Indeed, in most scientific arenas, singular behavior is viewed as an indication that the theory being used is deficient, at least in the sense that it is not adequate for modeling systems in the regime where such behavior is predicted Berry It is therefore common to claim that general relativity, in predicting that spacetime is singular, is predicting its own demise, and that classical descriptions of space and time break down at black hole singularities and the Big Bang, and all the rest Hawking and Ellis ; Hawking and Penrose Such a view denies that singularities are real features of the actual world, and rather asserts that they are merely artifacts of our current, inevitably limited, physical theories, marking the regime where the representational capacities of the theory at issue breaks down.

This attitude is widely adopted with regard to many important cases, e. No one seriously believes that singular behavior in such models in those classical theories represents truly singular behavior in the physical world. We should, the thought goes, treat singularities in general relativity in the same way. One of the most common arguments that incomplete paths and non-maximal spacetimes are physically unacceptable, and perhaps the most interesting one, coming as it does from physicists rather than from philosophers, invokes something very like the Principle of Sufficient Reason: if whatever creative force responsible for spacetime could have continued on to create more of it, what possible reason could there have been for it to have stopped at any particular point Penrose ; Geroch ?

An advocate of this viewpoint would argue that, from a point of view natural for general relativity, spacetime does not evolve at all. It just sits there, once and for all, as it were, a so-called block universe Putnam ; the entries Time Machines , Time Travel and Being and Becoming in Modern Physics. If it happens to sit there non-maximally, well, so be it.

This kind of response, however, has problems of its own, such as with the representation of our subjective experience, which seems inextricably tied up with ideas of evolution and change. One can produce other metaphysical arguments against the view that spacetime must be maximal.

To demand maximality may lead to Buridan's Ass problems, for it can happen that global extensions exist in which one of a given set of incomplete curves is extendible, but no global extension exists in which every curve in the set is extendible Ellis and Schmidt It is, in any event, difficult to know what to make of the invocation of such overtly metaphysical considerations in arguments in this most hard of all hard sciences.

See Curiel and Earman for critical survey of such arguments, and Doboszewski for a recent comprehensive survey of all these issues, including discussion of the most recent technical results. A common hope is that when quantum effects are taken into account in the vicinity of such extreme conditions of curvature where singularities are predicted by the classical theory, the singular nature of the spacetime geometry will be suppressed, leaving only well behaved spacetime structure.

Advocates of various programs of quantum gravity also argue that in such a complete, full theory, singularities of the kinds discussed here will not appear.

Recent important work by Wall a, b shows that these hopes face serious problems. We pick up these issues below, in section 5.

In any event, it is well to keep in mind that, even if singularities are observed one day, and we are able to detect regularity in their behavior of a sort that lends itself to formulation as physical law, it seems likely that this law will not be a consequence of general relativity but will rather go beyond its bounds in radical ways, for, as we have seen, general relativity by itself does not have any mechanism for constraining the possible behavior that singular structure of various types may manifest.

It is perhaps just this possibility that excites a frisson of pleasure in those of the libertine persuasion at the same time as it makes the prudish shudder with revulsion. For a philosopher, the issues mooted here offer deep and rich veins for those contemplating, among other matters: the role of explanatory power in the assessment of physical theories; the interplay among observation, mathematical models, physical intuition and metaphysical predilection in the genesis of scientific knowledge; questions about the nature of the existence attributable to physical entities in spacetime and to spacetime itself; and the role of mathematical models of physical systems in our understanding of those systems, as opposed to their role in the mere representation of our knowledge of them.

The simplest picture of a black hole is that of a system whose gravity is so strong that nothing, not even light, can escape from it. Systems of this type are already possible in the familiar Newtonian theory of gravity. The escape velocity of a body is the velocity at which an object would have to begin to travel to escape the gravitational pull of the body and continue flying out to infinity, without further acceleration. Because the escape velocity is measured from the surface of an object, it becomes higher if a body contracts and becomes more dense.

Under such contraction, the mass of the body remains the same, but its surface gets closer to its center of mass; thus the gravitational force at the surface increases. If the object were to become sufficiently dense, the escape velocity could therefore exceed the speed of light, and light itself would be unable to escape.

This much of the argument makes no appeal to relativistic physics, and the possibility of such Newtonian black holes was noted in the late 18th Century by Michell and Laplace , part ii , p. These Newtonian objects, however, do not precipitate the same sense of crisis as do relativistic black holes. Although light emitted at the surface of the collapsed body cannot escape, a rocket with powerful enough motors firing could still push itself free.

It just needs to keep firing its rocket engines so that the thrust is equal to or slightly greater than the gravitational force. Since in Newtonian physics there is no upper bound on possible velocities, moreover, one could escape simply by being fired off at an initial velocity greater than that of light. Taking relativistic considerations into account, however, we find that black holes are far more exotic entities.

Given the usual understanding that relativity theory rules out any physical process propagating faster than light, we conclude that not only is light unable to escape from such a body: nothing would be able to escape this gravitational force.

That includes the powerful rocket that could escape a Newtonian black hole. Further, once the body has collapsed down to the point where its escape velocity is the speed of light, no physical force whatsoever could prevent the body from continuing to collapse further, for that would be equivalent to accelerating something to speeds beyond that of light.

Thus once this critical point of collapse is reached, the body will get ever smaller, more and more dense, without limit. It has formed a relativistic black hole.

Here is where the intimate connection between black holes and singularities appears, for general relativity predicts that, under physically reasonable and generic conditions, a spacetime singularity will form from the collapsing matter once the critical point of black-hole formation is reached Penrose ; Schoen and Yau ; Wald For any given body, this critical stage of unavoidable collapse occurs when the object has collapsed to within its so-called Schwarzschild radius, which is proportional to the mass of the body.

Our sun has a Schwarzschild radius of approximately three kilometers; the Earth's Schwarzschild radius is a little less than a centimeter; the Schwarzschild radius of your body is about 10 cm—ten times smaller than a neutrino and 10 10 times smaller than the scale characteristic of quark interactions. This means that if you could collapse all the Earth's matter down to a sphere the size of a pea, it would form a black hole. It is worth noting, however, that one does not need an extremely high density of matter to form a black hole if one has enough mass.

If all the stars in the Milky Way gradually aggregate towards the galactic center while keeping their proportionate distances from each other, they will all fall within their joint Schwarzschild radius and so form a black hole long before they are forced to collide.

In this case, of course, the water would indeed eventually collapse on itself to arbitrarily high densities.

Some supermassive black holes at the centers of galaxies are thought to be even more massive than the example of the water, at several billion solar masses, though in these cases the initial density of the matter thought to have formed the black holes was extraordinarily high. According to the standard definition Hawking and Ellis ; Wald , the event horizon of a black hole is the surface formed by the points of no return.

That is, it is the boundary of the collection of all events in the spacetime closest to the singularity at which a light signal can still escape to the external universe. Everything including and inside the event horizon is the black hole itself.

See section 3. For a standard uncharged, non-rotating black hole, the event horizon lies at the Schwarzschild radius. A flash of light that originates at an event inside the black hole will not be able to escape, but will instead end up in the central singularity of the black hole. A light flash originating at an event outside of the event horizon will escape unless it is initially pointed towards the black hole , but it will be red-shifted strongly to the extent that it started near the horizon.

An outgoing beam of light that originates at an event on the event horizon itself, by definition, remains on the event horizon until the temporal end of the universe. General relativity tells us that clocks running at different locations in a gravitational field will, in a sense that can be made precise, generally not agree with one another.

In the case of a black hole, this manifests itself in the following way. Imagine someone falls into a black hole, and, while falling, she flashes a light signal to us every time her watch hand ticks. Observing from a safe distance outside the black hole, we would find the times between the arrival of successive light signals to grow larger without limit, because it takes longer for the light to escape the black hole's gravitational potential well the closer to the event horizon the light is emitted.

This is the red-shifting of light close to the event horizon. That is, it would appear to us that time were slowing down for the falling person as she approached the event horizon. The ticking of her watch and every other process as well would seem to go ever more slowly as she approached ever more closely to the event horizon.

This talk of seeing the person is somewhat misleading, because the light coming from the person would rapidly become severely red-shifted, and soon would not be practically detectable. From the perspective of the infalling person, however, nothing unusual happens at the event horizon. She would experience no slowing of clocks, nor see any evidence that she is passing through the event horizon of a black hole.

Her passing the event horizon is simply the last moment in her history at which a light signal she emits would be able to escape from the black hole. The concept of an event horizon is a global one that depends on the overall structure of the spacetime, and in particular on how processes physically evolve into the indefinite future. Locally there is nothing noteworthy about the points on the event horizon.

In particular, locating the event horizon by any combination of strictly local measurements is impossible in principle , no matter how ingeniously the instruments are arranged and precisely the measurements made.

The presence of an event horizon in this global sense is a strictly unverifiable hypothesis. One need not be a verificationist about scientific knowledge to be troubled by this state of affairs Curiel How should a good empiricist feel about all of this? The global and geometrical nature of black holes also raises interesting questions about the sense in which one may or should think of them as physical objects or systems Curiel These are what we call the black holes: a point of infinite density, surrounded by an event horizon located at the Schwarzschild radius.

The event horizon "protects" the singularity, preventing outside observers from seeing it unless they traverse the event horizon, according to Quanta Magazine. Physicists long thought that in GR, all singularities like this are surrounded by event horizons, and this concept was known as the Cosmic Censorship Hypothesis — so named because it was surmised that some process in the universe prevented or "censored" singularities from being viewable.

However, computer simulations and theoretical work have raised the possibility of exposed or "naked" singularities. A naked singularity would be just that: a singularity without an event horizon, fully observable from the outside universe.

Whether such exposed singularities exist continues to be a subject of considerable debate. Because they are mathematical singularities, nobody knows what's really at the center of a black hole. To understand it, we need a theory of gravity beyond GR. Specifically, we need a quantum theory of gravity, one that can describe the behavior of strong gravity at very tiny scales, according to Physics of the Universe.

Hypotheses that modify or replace general relativity to give us a replacement of the black hole singularity include Planck stars a highly-compressed exotic form of matter , gravastars a thin shell of matter supported by exotic gravity , and dark energy stars an exotic state of vacuum energy that behaves like a black hole.

To date, all these ideas are hypothetical, and a true answer must await a quantum theory of gravity. The Big Bang theory, which assumes general relativity to be true, is the modern cosmological model of the history of the universe.