Spherically symmetric spacetimeIn physics, spherically symmetric spacetimes are commonly used to obtain analytic and numerical solutions to Einstein's field equations in the presence of radially moving matter or energy. Because spherically symmetric spacetimes are by definition irrotational, they are not realistic models of black holes in nature. However, their metrics are considerably simpler than those of rotating spacetimes, making them much easier to analyze.
Exact solutions in general relativityIn general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.
Non-standard cosmologyA non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term non-standard is applied to any theory that does not conform to the scientific consensus. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would be in 2010.
Cosmic timeCosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). The clocks measuring cosmic time should move along the Hubble flow.
Willem de SitterWillem de Sitter (6 May 1872 – 20 November 1934) was a Dutch mathematician, physicist, and astronomer. Born in Sneek, de Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa (1897–1899). Then, in 1908, de Sitter was appointed to the chair of astronomy at Leiden University. He was director of the Leiden Observatory from 1919 until his death. De Sitter made major contributions to the field of physical cosmology.
Alternatives to general relativityAlternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity. There have been many different attempts at constructing an ideal theory of gravity. These attempts can be split into four broad categories based on their scope. In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification.
General relativityGeneral relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime.
Spacetime symmetriesSpacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important in simplifying solutions to many problems. Spacetime symmetries are used in the study of exact solutions of Einstein's field equations of general relativity. Spacetime symmetries are distinguished from internal symmetries. Physical problems are often investigated and solved by noticing features which have some form of symmetry.
Kerr metricThe Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find. The Kerr metric is a generalization to a rotating body of the Schwarzschild metric, discovered by Karl Schwarzschild in 1915, which described the geometry of spacetime around an uncharged, spherically symmetric, and non-rotating body.
Static spherically symmetric perfect fluidIn metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure. Such solutions are often used as idealized models of stars, especially compact objects such as white dwarfs and especially neutron stars.
