Gravitational singularity

As a singularity is called in physics and astronomy states in which, for example, the considered space-times (among their metrics) can no longer be defined in a single point or a complex manifold.

You are first only as mathematical singularities formulated and depend, inter alia, of special mass values ​​M, angular momentum J, or other parameters, the question physical law is not defined, invalid and is not suitable to describe the circumstances eg for M → Mc (where Mc is a critical parameter value ). One can, however, specify suspected properties of a mathematical singularity in general, but do not know how the singular behavior is physically designed really - about: whatever " material " mentioned the manifold is. An infinitely small extent ( point) of a physical object or the divergence of a size to an infinite value contradicts the everyday experience. But singularities, non- point-like be, give about the space-time so much bends around the object that size information can not be put into a meaningful relationship with the metric of the ambient space.

Physical quantities are set by physical laws in relationship. In this case, the approach of the parameter to a certain value, seek a different size to infinity. That is, it is singular.

Types of singularities

There are two types of singularities:

• Real or intrinsic singularities and
• Coordinate singularities.

The latter can be obtained by choosing an appropriate coordinate system to exclude, for real singularities this is not possible, here's a new theory ( law of physics ) is needed.

Astrophysics and Cosmology

In astrophysics and cosmology, the term is often used synonymously for singularity or black holes in the Big Bang theory of the initial singularity. The field equations of general relativity are the figures used to explain physical laws in both cases. For the initial singularity that do not exist in their time and space. Thus, information about it is meaningless, how big it was or how long it was. Black holes can be applied to characterize them by their action surrounding space-time. Many properties of the singularity inside the black hole, such as its density, but are similar undefined as the initial singularity.

Karl Schwarzschild was the first that could offer a solution ( exterior Schwarzschild solution ) for the field equations. His solution describes in reality, the non-existent non-rotating, ie static black holes and the central point singular ( point singularity ). In the Kruskal coordinates is a manifold described by a hyperboloid from the point of singularity. It looks so explicitly, that here at the event horizon itself no singularity occurs ( see, however, the following).

Only in 1963 did the New Zealand mathematician Roy Kerr found another solution ( Kerr solution ) for rotating black holes, which is singular in a one-dimensional ring in the equatorial plane. The radius of the ring singularity corresponds to the Kerr parameter. A more general solution with an additional electric point charge leads to the Kerr-Newman metric.

The exterior Schwarzschild solution is a special case of the Kerr solution ( Kerr parameter "a = 0 ", ie no rotation ). For maximum rotating black holes, that is, when the event horizon is rotating at the speed of light, on the other hand is "a = 1" and the event horizon ( the gravitational radius) is now a ring singularity.

The Bang theories, in contrast, not a point in space, but in a point of time ( " t = 0") is singular. So you do not describe the Big Bang itself, but only the evolution of the universe after ( from the age of about 10-43 seconds).

The general theory of relativity ( Einstein's theory of gravity ) is a " classical theory ", no quantum theory, therefore it loses on very small length scales ( Planck length) to be valid and it will start the domain of quantum gravity. However, very little is known about the internal condition or the establishment of singularities within the scope of these theories.

• Astrophysics
• General Theory of Relativity