A wormhole is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.
The following is a timeline of gravitational physics and general relativity.
In Einstein's theory of general relativity, the Schwarzschild metric is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916.
The Friedmann–Lemaître–Robertson–Walker metric is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.
The 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.
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity. The theory was first proposed by Élie Cartan in 1922. Einstein–Cartan theory is the simplest Poincaré gauge theory.
The Kerr–Newman metric is the most general asymptotically flat and stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged and rotating mass. It generalizes the Kerr metric by taking into account the field energy of an electromagnetic field, in addition to describing rotation. It is one of a large number of various different electrovacuum solutions; that is, it is a solution to the Einstein–Maxwell equations that account for the field energy of an electromagnetic field. Such solutions do not include any electric charges other than that associated with the gravitational field, and are thus termed vacuum solutions.
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric. The converse of the theorem is true and is called Israel's theorem. The converse is not true in Newtonian gravity.
Ronald Kantowski is a theoretical cosmologist, well known in the field of general relativity as the author, together with Rainer K. Sachs, of the Kantowski–Sachs dust solutions to the Einstein field equation. These are a widely used family of inhomogeneous cosmological models.
The Einstein radius is the radius of an Einstein ring, and is a characteristic angle for gravitational lensing in general, as typical distances between images in gravitational lensing are of the order of the Einstein radius.
In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modeled by general relativity. The equation is
An inhomogeneous cosmology is a physical cosmological theory which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces enough to skew our view of the Universe. When the universe began, matter was distributed homogeneously, but over billions of years, galaxies, clusters of galaxies, and superclusters have coalesced, and must, according to Einstein's theory of general relativity, warp the space-time around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies claimed in 1998-1999 that high redshift supernovae were further away than our calculations showed they should be, it was suggested that the expansion of the universe is accelerating, and dark energy, a repulsive energy inherent in space, was proposed to explain the acceleration. Dark energy has since become widely accepted, but it remains unexplained. Accordingly, some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.
While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak lensing regime, in which the deflection is impossible to detect in a single background source. However, even in these cases, the presence of the foreground mass can be detected, by way of a systematic alignment of background sources around the lensing mass. Weak gravitational lensing is thus an intrinsically statistical measurement, but it provides a way to measure the masses of astronomical objects without requiring assumptions about their composition or dynamical state.
In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. Unlike a flat-space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime. The Nariai limit has no singularities, the cosmological and black hole horizons have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch.
The Virbhadra-Ellis lens equation in astronomy and mathematics relates to the angular positions of an unlensed source , the image , the Einstein bending angle of light , and the angular diameter lens-source and observer-source distances.
Photon sphere (definition):
A photon sphere of a static spherically symmetric metric is a timelike hypersurface if the deflection angle of a light ray with the closest distance of approach diverges as
Relativistic images are images of gravitational lensing which result due to light deflections by angles .
A black hole cosmology is a cosmological model in which the observable universe is the interior of a black hole. Such models were originally proposed by theoretical physicist Raj Pathria, and concurrently by mathematician I. J. Good.
In Einstein's theory of general relativity, the interior Schwarzschild metric is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid and has zero pressure at the surface. This is a static solution, meaning that it does not change over time. It was discovered by Karl Schwarzschild in 1916, who earlier had found the exterior Schwarzschild metric.
