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Effective One-body Formalism
The effective one-body or EOB approach is an analytical approach to the gravitational two-body problem in general relativity. It was introduced by Alessandra Buonanno and Thibault Damour in 1999. It aims to describe all different phases of the two-body dynamics in a single analytical method. Classical gravity theory allows analytical calculations to be made in particular limits, such as post-Newtonian theory in the early inspiral, when the objects are at large separation, or black hole perturbation theory, when the two objects differ greatly in mass. In addition, they lead to results faster than numerical relativity. Rather than being considered distinct from these independent approaches to the two-body problem, the EOB approach is a way to resum information from other independent methods. It does so by mapping the general two-body problem to that of a test particle in an effective metric. The EOB approach was used in the data analysis of gravitational wave detectors such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GR2bodyparameterspace
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Two-body Problem
In classical mechanics, the two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles. The problem assumes that the two objects interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. The most prominent case of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions. A simpler "one body" model, the " central-force problem", treats one object as the immobile source of a force acting on the other. One then seeks to predict the motion of the single remaining mobile object. Such an approximation can give useful results when one object is much more massive than the other (as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
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 ' 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. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alessandra Buonanno
Alessandra Buonanno is an Italian naturalized-American theoretical physicist and director at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam. She is the head of the "Astrophysical and Cosmological Relativity" department. She holds a research professorship at the University of Maryland, College Park, and honorary professorships at the Humboldt University in Berlin, and the University of Potsdam. She is a leading member of the LIGO Scientific Collaboration, which observed gravitational waves from a binary black-hole merger in 2015. Early life and education Buonanno earned her MSc in 1993, and she completed her PhD in theoretical physics at the University of Pisa in 1996. After a brief period spent at the theory division of CERN, she held a postdoctoral position at the Institut des Hautes Etudes Scientifiques (IHES) in France and the R.C. Tolman Prize Fellowship at the California Institute of Technology. Career and research Buonanno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thibault Damour
Thibault Damour (; born 7 February 1951) is a French physicist. He was a permanent professor in theoretical physics at the Institut des Hautes Études Scientifiques (IHÉS) from 1989 to 2022. Since then, he is professor emeritus. An expert in general relativity, he has long taught this theory at the École Normale Supérieure (Ulm). He contributed greatly to the modelling of gravitational waves from compact binary systems, and with Alessandra Buonanno, he invented the "effective one-body" approach to representing the orbital trajectories of binary black holes. In 2021 he was awarded, with Alessandra Buonanno, the Balzan Prize The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the br ... for Gravitation: physical and astrophysical aspects as well as the Galileo Galilei Medal and the Dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post-Newtonian
In general relativity, the post-Newtonian expansions (PN expansions) are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher order terms can be added to increase accuracy, but for strong fields sometimes it is preferable to solve the complete equations numerically. This method is a common mark of effective field theories. In the limit, when the small parameters are equal to 0, the post-Newtonian expansion reduces to Newton's law of gravity. Expansion in 1/''c''2 The post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of the matter that creates the gravitational field, to the speed of light, which in this case is more precisely called the ''speed of gravity''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearized Gravity
In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized gravity is integral to the study of gravitational waves and weak-field gravitational lensing. Weak-field approximation The Einstein field equation (EFE) describing the geometry of spacetime is given as (using natural units) :R_ - \fracRg_ = 8\pi GT_ where R_ is the Ricci tensor, R is the Ricci scalar, T_ is the energy–momentum tensor, and g_ is the spacetime metric tensor that represent the solutions of the equation. Although succinct when written out using Einstein notation, hidden within the Ricci tensor and Ricci scalar are exceptionally nonlinear dependencies on the metric which render the prospect of finding exact solutions impractical in most systems. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Relativity
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 governed 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. Overview A primary goal of numerical relativity is to study spacetimes whose exact form is not known. The spacetimes so found computationally can either be fully dynamical, stationary or static and may contain matter fields or vacuum. In the case of stationary and static solutions, numerical methods may also be used to study the stability of the equilibrium spacetimes. In the case of dynamical spacetimes, the problem may be divided into the initial value problem and the evolution, each requiring different methods. Numeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padé Approximant
In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed around 1890 by Henri Padé, but goes back to Georg Frobenius, who introduced the idea and investigated the features of rational approximations of power series. The Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. For these reasons Padé approximants are used extensively in computer calculations. They have also been used as auxiliary functions in Diophantine approximation and transcendental number theory, though for sharp results ad hoc methods— in some sense inspired by the Padé theory— typically replace them. Since Padé approximant is a rational function, an artificial singul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Tensor (general Relativity)
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. Notation and conventions Throughout this article we work with a metric signature that is mostly positive (); see sign convention. The gravitation constant G will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over. Definition Mathematically, spacetime is represented by a four-dimensional differentiable manifold M and the metric tensor is given as a covariant, second-degree, symmetric tensor on M, conventionally denoted by g. Moreover, the metric is required to be nondegenera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational-wave Observatory
A gravitational-wave detector (used in a gravitational-wave observatory) is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built and constantly improved. The present-day generation of laser interferometers has reached the necessary sensitivity to detect gravitational waves from astronomical sources, thus forming the primary tool of gravitational-wave astronomy. The first direct detection of gravitational waves made in 2015 by the Advanced LIGO observatories, a feat which was awarded the 2017 Nobel Prize in Physics. Challenge The direct detection of gravitational waves is complicated by the extraordinarily small effect the waves produce on a detector. The amplitude of a spherical wave falls off as the inverse of the distance from the source. Thus, even waves from extreme systems such as merging binary black holes die out to a very small amplitude by the time they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large observatories were built in the United States with the aim of detecting gravitational waves by laser interferometry. These observatories use mirrors spaced four kilometers apart which are capable of detecting a change of less than one ten-thousandth the charge diameter of a proton. (that is, to Proxima Centauri at ). The initial LIGO observatories were funded by the United States National Science Foundation (NSF) and were conceived, built and are operated by Caltech and MIT. They collected data from 2002 to 2010 but no gravitational waves were detected. The Advanced LIGO Project to enhance the original LIGO detectors began in 2008 and continues to be supported by the NSF, with important contributions from the United Kingdom's Science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
