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General relativity, also known as the general theory of relativity, and as 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. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever present matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.
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 general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961.
John Lighton Synge was an Irish mathematician and physicist, whose seven-decade career included significant periods in Ireland, Canada, and the USA. He was a prolific author and influential mentor, and is credited with the introduction of a new geometrical approach to the theory of relativity.
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term.
The Kerr–Newman metric describes the spacetime geometry around a mass which is electrically charged and rotating. It is a vacuum solution which generalizes the Kerr metric by additionally taking into account the energy of an electromagnetic field, making it the most general asymptotically flat and stationary solution of the Einstein–Maxwell equations in general relativity. As an electrovacuum solution, it only includes those charges associated with the magnetic field; it does not include any free electric charges.
In 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.
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
Roy Patrick Kerr is a New Zealand mathematician who discovered the Kerr geometry, an exact solution to the Einstein field equation of general relativity. His solution models the gravitational field outside an uncharged rotating massive object, including a rotating black hole. His solution to Einstein's equations predicted spinning black holes before they were discovered.
Ezra Theodore Newman was an American physicist, known for his many contributions to general relativity theory. He was professor emeritus at the University of Pittsburgh. Newman was awarded the 2011 Einstein Prize from the American Physical Society.
The Goldberg–Sachs theorem is a result in Einstein's theory of general relativity about vacuum solutions of the Einstein field equations relating the existence of a certain type of congruence with algebraic properties of the Weyl tensor.
In theoretical physics, Whitehead's theory of gravitation was introduced by the mathematician and philosopher Alfred North Whitehead in 1922. While never broadly accepted, at one time it was a scientifically plausible alternative to general relativity. However, after further experimental and theoretical consideration, the theory is now generally regarded as obsolete.
The mathematics of general relativity is complicated. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the speed of light, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates.
Jürgen Ehlers was a German physicist who contributed to the understanding of Albert Einstein's theory of general relativity. From graduate and postgraduate work in Pascual Jordan's relativity research group at Hamburg University, he held various posts as a lecturer and, later, as a professor before joining the Max Planck Institute for Astrophysics in Munich as a director. In 1995, he became the founding director of the newly created Max Planck Institute for Gravitational Physics in Potsdam, Germany.
Engelbert Levin Schücking, in English-language works often cited as E. L. Schucking, was a physics professor at New York University in New York City. His research interests were theoretical astrophysics, general relativity, and cosmology.
Complex spacetime is a mathematical framework that combines the concepts of complex numbers and spacetime in physics. In this framework, the usual real-valued coordinates of spacetime are replaced with complex-valued coordinates. This allows for the inclusion of imaginary components in the description of spacetime, which can have interesting implications in certain areas of physics, such as quantum field theory and string theory.
Ivor Robinson was a British-American mathematical physicist, born and educated in England, noted for his important contributions to the theory of relativity. He was a principal organizer of the Texas Symposium on Relativistic Astrophysics.
In general relativity and tensor calculus, the contracted Bianchi identities are:
Kerr–Schild perturbations are a special type of perturbation to a spacetime metric which only appear linearly in the Einstein field equations which describe general relativity. They were found by Roy Kerr and Alfred Schild in 1965.
References
- ↑ Ferreira, Pedro G. (2014). The Perfect Theory: A Century of Geniuses and the Battle over General Relativity . Houghton Mifflin Harcourt. p. 114. ISBN 9780547554907 . Retrieved 27 March 2019.
- ↑ Synge, J. L. & Schild, A. (1949). Tensor Calculus. University of Toronto Press. ISBN 0-8020-1031-8. OCLC 6007241.
- ↑ John DeCicco (1951 ) Review: J. L. Synge & Alfred Schild Tensor Calculus, Bulletin of the American Mathematical Society 57(6):500–2 via Project Euclid
- ↑ Richard A. Matzner & L. C. Shepley (1982) Spacetime and Geometry: The Alfred Smith Lectures, page ix, University of Texas Press
- ↑ Engelbert Schücking (August 1989) The First Texas Symposium on Relativistic Astrophysics, Physics Today pages 46 to 52
- 1 2 3 Fulvio Melia (2009) Cracking the Einstein Code, University of Chicago Press ISBN 9780226519517
- ↑ Schucking, E. L. (1978). "Obituary. Alfred E. Schild". Physics Today. 31 (3): 79–80. Bibcode:1978PhT....31c..79S. doi: 10.1063/1.2994979 .
- ↑ Alfred Schild Archived 2021-07-28 at the Wayback Machine from Department of Physics, University of Texas at Austin
