Solutions of the Einstein field equationsSolutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact.
Exact solutions in general relativityGeneral relativity G μ ν + Λ g μ ν = κ T μ ν {\displaystyle G_{\mu u }+\Lambda g_{\mu u }={\kappa }T_{\mu u }} Introduction HistoryTimelineTests Mathematical formulation Fundamental concepts Equivalence principle Special relativity World line Pseudo-Riemannian manifold Phenomena Kepler problem Gravitational lensing Gravitational redshift Gravitational time dilation Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor EquationsFormalisms Equations Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein Raychaudhuri Teukolsky Formalisms ADM NP BSSN Post-Newtonian Advanced theory Kaluza–Klein theory Quantum gravity Quantum field theory in curved spacetime Solutions Schwarzschild (interior) Reissner–Nordström Einstein–Rosen waves Wormhole Gödel Kerr Kerr–Newman Kerr–Newman–de Sitter Kasner Kantowski-Sachs Lemaître–Tolman Wahlquist Taub–NUT Milne Robertson–Walker Oppenheimer–Snyder pp-wave van Stockum dust Hartle–Thorne Vaidya Peres De Sitter-Schwarzschild McVittie Weyl Scientists Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedmann Milne Zwicky Lemaître Oppenheimer Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Raychaudhuri Taylor Hulse van Stockum Taub Newman Yau Thorne others Physics portal Categoryvte In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
Kasner metricSolution of Einstein field equations Figure 1. Dynamics of Kasner metrics eq. 2 in spherical coordinates towards singularity. The Lifshitz-Khalatnikov parameter is u=2 (1/u=0.5) and the r coordinate is 2pα(1/u)τ where τ is logarithmic time: τ = ln t. Shrinking along the axes is linear and uniform (no chaoticity).Gravitational singularityCondition in which spacetime itself breaks down General relativity G μ ν + Λ g μ ν = κ T μ ν {\displaystyle G_{\mu u }+\Lambda g_{\mu u }={\kappa }T_{\mu u }} Introduction HistoryTimelineTests Mathematical formulation Fundamental concepts Equivalence principle Special relativity World line Pseudo-Riemannian manifold Phenomena Kepler problem Gravitational lensing Gravitational redshift Gravitational time dilation Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor EquationsFormalisms Equations Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein Raychaudhuri Teukolsky Formalisms ADM NP BSSN Post-Newtonian Advanced theory Kaluza–Klein theory Quantum gravity Quantum field theory in curved spacetime Solutions Schwarzschild (interior) Reissner–Nordström Einstein–Rosen waves Wormhole Gödel Kerr Kerr–Newman Kerr–Newman–de Sitter Kasner Kantowski-Sachs Lemaître–Tolman Wahlquist Taub–NUT Milne Robertson–Walker Oppenheimer–Snyder pp-wave van Stockum dust Hartle–Thorne Vaidya Peres De Sitter-Schwarzschild McVittie Weyl Scientists Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedmann Milne Zwicky Lemaître Oppenheimer Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Raychaudhuri Taylor Hulse van Stockum Taub Newman Yau Thorne others Physics portal Categoryvte In theoretical physics, a gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically.
Friedmann–Lemaître–Robertson–Walker metricThe Friedmann–Lemaître–Robertson–Walker metric (FLRW; ) is a metric that describes a homogeneous, isotropic, expanding (or otherwise, contracting, oscillating or constant) 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.
Vladimir BelinskiVladimir Alekseevich Belinski (last name is also spelled Belinsky, Russian: Владимир Алексеевич Белинский; born 26 March 1941) is a Russian and Italian theoretical physicist involved in research in cosmology and general relativity. He worked at Landau Institute for Theoretical Physics from 1968 to 1989 and got his Habilitation (Doctor of Sciences) degree at this Institute in 1980.
AnisotropyAnisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength.
Isaak KhalatnikovIsaak Markovich KhalatnikovForMemRS (Ukrainian: Ісаак Маркович Халатников, romanized: Isaak Markovych Khalatnykov, Russian: Исаак Маркович Халатников; 17 October 1919 – 9 January 2021) was a Soviettheoretical physicist who made significant contributions to many areas of theoretical physics, including general relativity, quantum field theory, and the theory of quantum liquids.Evgeny LifshitzEvgeny Mikhailovich Lifshitz (Russian: Евгений Михайлович Лифшиц; Ukrainian: Євген Михайлович Ліфшиць, romanized: Yevhen Mykhailovych Lifshyts; 21 February 1915 – 29 October 1985) was a Soviet physicist and brother of the physicist Ilya Lifshitz.
Landau Institute for Theoretical PhysicsThe L. D. Landau Institute for Theoretical Physics (Russian: Институт теоретической физики имени Л. Д. Ландау (ИТФ)) of the Russian Academy of Sciences is a research institution, located in the small town of Chernogolovka near Moscow (there is also a subdivision in Moscow, on the territory of the P. L. Kapitza Institute for Physical Problems).
Chronology of the universeHistory and future of the universe
Quantum chaosQuantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of the Planck constant to the action of the system tends to zero.*As an Amazon Associate I earn from qualifying purchases.