General 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. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
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, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. The origin of this idea can be found in an English mathematician William Kingdon Clifford's works. This theory was enthusiastically promoted by John Wheeler in the 1960s, and work on it continues in the 21st century.
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 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.
The Max Planck Institute for Gravitational Physics is a Max Planck Institute whose research is aimed at investigating Einstein's theory of relativity and beyond: Mathematics, quantum gravity, astrophysical relativity, and gravitational-wave astronomy. The institute was founded in 1995 and is located in the Potsdam Science Park in Golm, Potsdam and in Hannover where it closely collaborates with the Leibniz University Hannover. Both the Potsdam and the Hannover parts of the institute are organized in three research departments and host a number of independent research groups.
The Arnowitt–Deser–Misner (ADM) formalism is a Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity. It was first published in 1959.
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 concept of mass in general relativity (GR) is more subtle to define than the concept of mass in special relativity. In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions that are applicable under different circumstances. Under some circumstances, the mass of a system in general relativity may not even be defined.
Charles William Misner was an American physicist and one of the authors of Gravitation. His specialties included general relativity and cosmology. His work has also provided early foundations for studies of quantum gravity and numerical relativity.
General Relativity is a graduate textbook and reference on Albert Einstein's general theory of relativity written by the gravitational physicist Robert Wald.
The initial value formulation of general relativity is a reformulation of Albert Einstein's theory of general relativity that describes a universe evolving over time.
Stanley Deser was an American physicist known for his contributions to general relativity. He was an emeritus Ancell Professor of Physics at Brandeis University in Waltham, Massachusetts and a senior research associate at California Institute of Technology.
A relativistic star is a rotating star whose behavior is well described by general relativity, but not by classical mechanics. The first such object to be identified was radio pulsars, which consist of rotating neutron stars. Rotating supermassive stars are a hypothetical form of a relativistic star. Relativistic stars are one possible source to allow gravitational waves to be studied.
A binary black hole (BBH), or black hole binary, is a system consisting of two black holes in close orbit around each other. Like black holes themselves, binary black holes are often divided into stellar binary black holes, formed either as remnants of high-mass binary star systems or by dynamic processes and mutual capture; and binary supermassive black holes, believed to be a result of galactic mergers.
In theoretical physics, shape dynamics is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general relativity and quantum mechanics.
Stuart Louis Shapiro is an American theoretical astrophysicist, who works on numerical relativity with applications in astrophysics, specialising in compact objects such as neutron stars and black holes.
Thomas W. Baumgarte is a German physicist specializing in the numerical simulation of compact objects in general relativity.
In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; instabilities offer insight into high-dimensional chaos and turbulence.
The Binary Black Hole Grand Challenge Alliance was a scientific collaboration of international physics institutes and research groups dedicated to simulating the sources and predicting the waveforms for gravitational waves, in anticipation of gravitational radiation experiments such as LIGO.
