Approximation methods in gravitational-radiation theory

1986 ◽  
Vol 64 (2) ◽  
pp. 140-145 ◽  
Author(s):  
Clifford M. Will
Keyword(s):  
Gravitational Radiation ◽  
Normal Modes ◽  
Slow Motion ◽  
Radiation Reaction ◽  
Weak Field ◽  
Approximation Methods ◽  
Binary Pulsar ◽  
Radiation Theory ◽  
Recent Developments ◽  
Reaction Forces

The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. We summarize recent developments in two areas in which approximations are important: (a) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel–Kramers–Brillouin approximation gives accurate estimates of the complex frequencies of the modes.

scholarly journals Analytic approximations in GR and gravitational waves

2019 ◽  
Vol 28 (06) ◽  
pp. 1930011 ◽  
Author(s):  
Luc Blanchet
Keyword(s):  
Binary Systems ◽  
State Of The Art ◽  
Equations Of Motion ◽  
Slow Motion ◽  
Weak Field ◽  
Analytic Approximation ◽  
Compact Binary ◽  
Recent Developments ◽  
Motion Approximation ◽  
Self Force

Analytic approximation methods in general relativity play a very important role when analyzing the gravitational wave signals recently discovered by the LIGO and Virgo detectors. In this contribution, we present the state of the art and some recent developments in the famous post-Newtonian (PN) or slow-motion approximation, which has successfully computed the equations of motion and the early inspiral phase of compact binary systems. We discuss also some interesting interfaces between the PN and the gravitational self-force (GSF) approach based on black-hole perturbation theory, and between PN and the post-Minkowskian (PM) approximation, namely a nonlinearity expansion valid for weak field and possibly fast-moving sources.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

scholarly journals Gravitational radiation and the binary pulsar

Nature ◽  
1982 ◽  
Vol 297 (5865) ◽  
pp. 357-358 ◽  
Author(s):  
Virginia Trimble
Keyword(s):  
Gravitational Radiation ◽  
Binary Pulsar

Classical tunneling as a consequence of radiation reaction forces

1997 ◽  
Vol 56 (3) ◽  
pp. 3624-3627 ◽  
Author(s):  
Frederik Denef ◽  
Joris Raeymaekers ◽  
Urban M. Studer ◽  
Walter Troost
Keyword(s):  
Radiation Reaction ◽  
Reaction Forces

scholarly journals The Stability of Relativistic Systems

1974 ◽  
Vol 64 ◽  
pp. 63-81
Author(s):  
S. Chandrasekhar
Keyword(s):  
Azimuthal Angle ◽  
Normal Modes ◽  
Radiation Reaction ◽  
Axisymmetric Deformation ◽  
Alternative Proof ◽  
Newtonian Theory ◽  
Relativistic Systems ◽  
The Stability

The stability of relativistic systems is reviewed against the background of what is known in the corresponding contexts of the Newtonian theory. In particular, the importance of determining whether Dedekind-like points of bifurcation occur along given stationary axisymmetric sequences is emphasized: the occurrence of such points of bifurcation may signal the onset of secular instability induced by radiation-reaction. (At a Dedekind-like point of bifurcation, the system can be subject, quasistationarily, to a non-axisymmetric deformation with an e2iϕ-dependence on the azimuthal angle ϕ.)A formalism is described in terms of which the normal modes of axisymmetric oscillation of axisymmetric systems can be determined. Specialized to neutral modes of oscillation the formalism provides an alternative proof of Carter's theorem and clarifies the minimal requirements for its validity. A parallel formalism is described for ascertaining whether an axisymmetric system can be subject to a quasi-stationary non-axisymmetric deformation. The possibility of applying this latter formalism to determining whether a Dedekind-like point of bifurcation occurs along the Kerr sequence is considered.

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