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Gravitational singularity is a point or region in spacetime.

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Gravitational singularity is often associated with black holes. A singularity as related to physics is a point or region in Spacetime in which gravitational forces cause matter to have an infinite density and zero Volume; associated with black holes.

Background of gravitational singularity.

Gravitational Singularity.
Many theories in physics have gravitational Singularity of one kind or another.

Many theories in physics have mathematical singularities of one kind or another, in which the equations predict that the rate of change of some quantity becomes infinite or increases without limit. This is generally viewed as a flaw in the theory. Even predictions of very large effects that are never observed may be thought of in the same manner. Although some physicists and more lay persons may believe in a particular kind of singularity, or indeed in multiple kinds, the true resolution of such paradoxes has so far always led to a new branch of physics and the awarding of multiple Nobel Prizes.

Well-known examples of this kind of problem include:

  • Olber's Paradox, a problem about the notion of a universe infinite in both space and time, with a uniform density of stars. A line in any direction must lead to the surface of a star, so the sky seen from Earth would have to be as bright as the Sun from horizon to horizon, and in fact planets couldn't exist. This is resolved by the Big Bang and the expanding universe. The microwave background radiation left over from the aftermath of the Big Bang was in fact as hot as the surface of a star in all directions (about 3000 K) when it formed, but it has cooled to less than a thousandth of that (2.73 K) and is now correspondingly dark.
  • The ultraviolet catastrophe in Classical physics, which Max Planck resolved using the quantum hypothesis, later confirmed and vastly extended in Quantum physics. Here the older theories predicted an infinite total rate of emission from black bodies in ultraviolet light and higher frequency electromagnetic radiation.
  • A point electron orbiting an atom in the Bohr model would be accelerated toward the nucleus, moving in a curved path, and would according to classical electromagnetic theory radiate away all of its energy of motion in a billionth of a second and fall into the nucleus. The Uncertainty Principle in quantum mechanics points out that there is no such thing as a point electron, makes it impossible to confine an electron in the space of a nucleus (a tiny fraction of its wavelength), and destroys the possibility of a continuous orbit. The Pauli Exclusion Principle requires different electrons in an atom to be in different quantum states, with different Spin, angular momentum, or other quantum numbers, and thus different spatial distributions of the probability of encountering them.
  • The infinite self-energy of a point electric charge in quantum mechanics was resolved through renormalization techniques in the Standard Model, and may be further resolved by string theory, in which electrons and other particles are not points. Some other answer not involving string theory may appear.

There are also coordinate singularities in many mathematical mappings, such as the fact that all directions from the North pole are equally South. The geometry at the North Pole is not singular; only the map is.

General relativity shows both coordinate singularities in metrics, and absolute singularities wherever a point mass turns up in the equations, usually in considering the evolution of a black hole. Changing to a different metric disposes of coordinate singularities. Getting rid of the infinite density, infinite force of gravity, and infinite curvature of space around a point mass requires changes in known physics.

The simplest route to a solution that we can imagine is of course to disallow point masses by one means or another. But by what means? Quantum theory has a suggestion (nothing can be squeezed into a space smaller than its wavelength), and string theory another (nothing can be smaller than the smallest dimension of spacetime). Unfortunately quantum theory is incompatible with General Relativity inside a black hole, and string theory is an infinite set of theories (infinite in a perfectly legitimate mathematical way), none of them currently capable of experimental test.

Popular explanation of gravitational singularity.

The spatial singularity is a theoretical term for the state of the center of a black hole. It would occur if matter could be compressed to infinitely small proportions, a mathematical point. This is the prediction of General Relativity if there is no physical limit on the size of particles. This has nothing to do with the formation of an Event horizon, which occurs as soon as the infalling matter is all inside its Schwarzchild radius, a relatively long time before it falls to the center.

Because nothing other than extremely random Hawking radiation can escape from beyond the Event horizon, there is no way to observe the core of a black hole, whether or not it is a singularity. The only physical properties we can currently apply to a black hole are mass (measured by the strength of the gravitational pull), volume (calculated in three dimensions using the Schwarzschild radius), electrical charge, temperature* (see notes), Spin, and magnetic field.

Gravitational singularity: Current Theoretical Limitations.

Although we possess compelling observational evidence for the existence of black holes, there is no physical evidence for spatial singularities. We have a certain amount of confidence in some predictions about matter falling into a black hole, but not a lot. For example, the Equation of state for the matter in a neutron star is very poorly known, and we have very little idea whether various kinds of exotic matter (strange matter, free quarks, H-dibaryons and so on) might form in the interior of a neutron star. Our current understanding tells us almost nothing about the kinds of matter that would form in the even denser, much higher energy conditions of a neutron star collapsing to a black hole, or of two neutron stars merging and forming a black hole.

There is no question that the equations of General Relativity in the absence of other physical limits on particle size require a singularity to form. That doesn't mean that it happens. It just means that we don't know enough physics to tell what happens.

It is frequently said that physics breaks down in the core of a black hole. This has been used as the basis for a multitude of fantasy novels, stories, TV shows, and movies, in which we are invited to suppose that what happens is whatever we (more particularly one or more characters in the tale) want. However, the premise is incorrect. What breaks down is not physics, but our understanding of physics. What happens proceeds according to the actual laws of physics, not according to what we fantasize in the absence of knowledge.

Detailed discussion of gravitational Singularity.

The definition of singularities as points where space-time curvature reaches infinity is the most obvious. However, singularities of other kinds can appear in a theory even if the curvature of space-time is finite everywhere. Not all geometries whose metric tensor blows up at some point must be actual geometric singularities; some of them are merely coordinate singularities and may be removed by a redefinition of coordinates.

More generally, a space-time is considered singular if it is geodesically incomplete, meaning that there are freely-falling observers whose existence is finite in at least one direction of time (as measured by their local clocks). For example, any observer below the Event horizon of a nonrotating black hole would fall into its center within a finite period of time, being pulled apart into particles whose nature we know nothing of, along with their clocks. We might want to describe this situation as a gravitational singularity in the center of the black hole. A beginning or end of time would clearly cut off all geodesics.

The points in spacetime where incomplete observers start and/or end their existences would then be singularities.

The simplest Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all timelike geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe of size 0 in all spatial dimensions, infinite density, infinite temperature, and infinite space-time curvature. However, the basic Big Bang model does not include quantum effects, and its predictions are valid only up to a point. At that point in the calculations, we are down to an astonishingly small size, high density, high temperature, and high curvature, but they are all finite, and the distance from there to infinity is, well, infinite.

Other physics can open up the model to a time before the Big Bang, which then evolves from a very small region of spacetime with a complete past, rather than from a point. In such models, multiple Big Bangs can evolve from regions in a much larger space. No tests of such models have been identified.

A singularity certainly exists in the geometry of pure General Relativity for its model of a black hole. In a non-rotating black hole (with rotation rate mathematically, and unphysically, exactly 0), the singularity occurs at a single point in the model coordinates, and is called a "point singularity". In a rotating black hole, often called a Kerr black hole, the singularity occurs on a ring, and is called a "ring singularity". Such a singularity may also theoretically become a wormhole**(see notes).

Until the early 1990s, it was widely believed that general relativity hides every singularity behind an Event horizon, making naked singularities impossible. This is referred to as the cosmic censorship hypothesis. However, in 1991 Shapiro and Teukolsky performed computer simulations of a rotating plane of dust which indicated that general relativity *might* allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed.

The singularity is an object that challenges many conventions in physics. This does not mean that it does not exist, but it does mean that it would take a new view and a few new theories about physics to explain its existence properly. It is believed that a theory of Quantum gravity, a theory that unifies General relativity with quantum mechanics, will eventually provide a better description of what actually occurs where General relativity by itself breaks down in a singularity. However, as of 2006, no theory of Quantum gravity has been experimentally confirmed. There are, however, a handful of promising theories in development. For more reading on the subject, see string theory (there are five types, with infinite variation), M-Theory (proposes to unify the string theories), Theory of everything.

Popular Culture

In the Stargate SG-1 episode 200, in a parody scene, it is mentioned that a singularity is about to explode. One of the characters even point out that this is impossible. This is used to great effect as a nod to scientific errors made in science fiction.

Notes about Gravitational Singularity.

  • See the discussion of entropy and Hawking radiation under black hole. Before Steven Hawking came up with the concept of Hawking radiation, the question of black holes having entropy was avoided. However, this concept demonstrates that black holes can radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore temperature. The loss of energy also suggests that black holes do not last forever, but rather "evaporate," slowly losing energy over millennia. Small black holes tend to be hotter whereas larger ones tend to be colder. All known black holes are so large that their temperature is far below that of the cosmic background radiation. Therefore they are currently all gaining energy, and will not begin to lose energy until we reach a cosmological redshift of more than a million, rather than the thousand or so since the background radiation formed.
  • If a rotating singularity is given a uniform electrical charge, a repellent force results, causing a ring singularity to form. The effect may be a stable wormhole, a non-point-like puncture in spacetime which may be connected to a second ring singularity on the other end. Although such wormholes are often suggested as routes for faster-than-light travel, such suggestions skip over the problem of getting out of the black hole at the other end, or even of surviving the immense tidal forces in the tightly curved interior of the wormhole.

Suggested reading on gravitational singularity.

1. The Elegant Universe by Brian Greene. This book provides a layperson's introduction to string theory, although some of the views expressed are already becoming outdated.

References to gravitational singularity.

  • Shapiro, S. L., and Teukolsky, S. A.: Formation of Naked Singularities: The Violation of Cosmic Censorship, Phys. Rev. Lett. 66, 994-997 (1991).
  • Wald, Robert M.: General Relativity, ch. 9, University of Chicago Press (1984).
  • Misner,Thorne, & Wheeler: Gravitation, Freeman (1973) The nonsingularity of the gravitational radius, and following sections; Global Techniques, Horizons, and Singularity Theorems.

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