Construction of the second-order gravitational perturbations produced by a compact object

Rosenthal, Eran

doi:10.1103/physrevd.73.044034

Cited by 42 publications

(65 citation statements)

References 25 publications

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“…The subleading selfacceleration a (2) ν has been computed in Refs. [84,85,86,87,88]. The accelerations a (1) ν and a (2) ν are independent of µ and thus depend only on x ν and u ν , or, equivalently, on q α andP i .…”

Section: F Rescaled Variables and Incorporation Of Backreaction On Tmentioning

confidence: 99%

Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion

2008

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Inspirals of stellar mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. Detection of these sources and extracting information from the signal relies on accurate theoretical models of the binary dynamics. We cast the equations describing binary inspiral in the extreme mass ratio limit in terms of action angle variables, and derive properties of general solutions using a two-timescale expansion. This provides a rigorous derivation of the prescription for computing the leading order orbital motion. As shown by Mino, this leading order or adiabatic motion requires only knowledge of the orbit-averaged, dissipative piece of the self force. The two timescale method also gives a framework for calculating the post-adiabatic corrections. For circular and for equatorial orbits, the leading order corrections are suppressed by one power of the mass ratio, and give rise to phase errors of order unity over a complete inspiral through the relativistic regime. These post-1-adiabatic corrections are generated by the fluctuating, dissipative piece of the first order self force, by the conservative piece of the first order self force, and by the orbit-averaged, dissipative piece of the second order self force. We also sketch a two-timescale expansion of the Einstein equation, and deduce an analytic formula for the leading order, adiabatic gravitational waveforms generated by an inspiral.

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Section: F Rescaled Variables and Incorporation Of Backreaction On Tmentioning

confidence: 99%

Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion

2008

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“…A formal expression for the second-order force has already been derived by Rosenthal [21,63]. However, he expresses the second-order force in a very particular gauge in which the first-order self-force vanishes.…”

Section: Prospects For a Global Solutionmentioning

confidence: 99%

“…[20,24]), the first-order external perturbation was assumed to be that of a point particle. This was justified to some extent by an argument first made by D'Eath [6,10] and later used by Rosenthal [63]. The argument is based on the integral Eq.…”

Section: The Metric Perturbation a Integral Formulation Of The Eimentioning

confidence: 99%

“…In Rosenthal's later derivations [63], this step was justified based on the notion that we are interested in the limit in which the small body shrinks to a point. However, if the size of the body vanishes, then so too does its mass, in which case there is no perturbation at all; and at second order, setting R to zero would create a divergent solution.…”

Section: The Metric Perturbation a Integral Formulation Of The Eimentioning

confidence: 99%

“…Second, it does not offer any way to go beyond first order, since it provides no means of determining the external perturbations (though see Refs. [21,63] for an extension to second order). Third, it is a somewhat weak result, with many if s in its construction.…”

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confidence: 99%

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Self-consistent gravitational self-force

2010

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I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.

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Self-force: Computational Strategies

Wardell

2015

Fundamental Theories of Physics

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Building on substantial foundational progress in understanding the effect of a small body's self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) modesum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.

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Construction of the second-order gravitational perturbations produced by a compact object

Cited by 42 publications

References 25 publications

Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion

Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion

Self-consistent gravitational self-force

Self-force: Computational Strategies

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