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 Large Scale Structure of Space–Time is a 1973 treatise on the theoretical physics of spacetime by the physicist Stephen Hawking and the mathematician George Ellis. It is intended for specialists in general relativity rather than newcomers.
Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory, LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation, one of several alternatives to general relativity. The theory was first proposed by Élie Cartan in 1922.
The history of loop quantum gravity spans more than three decades of intense research.
Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars. This work spurred the purely mathematical development of differential geometry.
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. The term pp stands for plane-fronted waves with parallel propagation, and was introduced in 1962 by Jürgen Ehlers and Wolfgang Kundt.
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.
Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and many other phenomena described by Albert Einstein's theory of general relativity. A currently active field of research in numerical relativity is the simulation of relativistic binaries and their associated gravitational waves.
Alfred Schild was a leading Austrian American physicist, well known for his contributions to the Golden age of general relativity (1960–1975).
James W. York Jr. was an American mathematical physicist who contributed to the theory of general relativity. In any physical theory, it is important to understand when solutions to the fundamental field equation exist, and answering this question was a theme of York's scientific work, with Yvonne Choquet-Bruhat, of formulating the Einstein field equation as a well-posed system in the sense of the theory of partial differential equations.
This is a list of contributors to the mathematical background for general relativity. For ease of readability, the contributions are unlinked but can be found in the contributors' article.
In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity. It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by Bryce DeWitt in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann using the so-called canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac. Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed gauge choice. Newer approaches based in part on the work of DeWitt and Dirac include the Hartle–Hawking state, Regge calculus, the Wheeler–DeWitt equation and loop quantum gravity.
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.
Robert Geroch is an American theoretical physicist and professor at the University of Chicago. He has worked prominently on general relativity and mathematical physics and has promoted the use of category theory in mathematics and physics. He was the Ph.D. supervisor for Abhay Ashtekar, Basilis Xanthopoulos and Gary Horowitz. He also proved an important theorem in spin geometry.
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.
In theoretical physics, a dynamical horizon (DH) is a local description of evolving black-hole horizons. In the literature there exist two different mathematical formulations of DHs—the 2+2 formulation developed first by Sean Hayward and the 3+1 formulation developed by Abhay Ashtekar and others. It provides a description of a black hole that is evolving. A related formalism, for black holes with zero influx, is an isolated horizon.
Corinne Alison Manogue is an American physicist who has worked in general relativity, mathematical physics, and physics education. She was elected a Fellow of the American Physical Society in 2005, and was an inaugural Fellow of the American Association of Physics Teachers in 2014.
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.
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