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#### Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge

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1009.4876

(Preprint), 297KB

PRD83_064018.pdf

(Any fulltext), 249KB

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##### Citation

Shah, A., Keidl, T., Friedman, J., Kim, D.-H., & Price, L. (2011). Conservative,
gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge.*
Physical Review D,* *83*(6): 064018. doi:10.1103/PhysRevD.83.064018.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-08F7-F

##### Abstract

This is the second of two companion papers on computing the self-force in a
radiation gauge; more precisely, the method uses a radiation gauge for the
radiative part of the metric perturbation, together with an arbitrarily chosen
gauge for the parts of the perturbation associated with changes in black-hole
mass and spin and with a shift in the center of mass. We compute the
conservative part of the self-force for a particle in circular orbit around a
Schwarzschild black hole. The gauge vector relating our radiation gauge to a
Lorenz gauge is helically symmetric, implying that the quantity h_{\alpha\beta}
u^\alpha u^\beta (= h_{uu}) must have the same value for our radiation gauge as
for a Lorenz gauge; and we confirm this numerically to one part in 10^{13}. As
outlined in the first paper, the perturbed metric is constructed from a Hertz
potential that is in term obtained algebraically from the the retarded
perturbed spin-2 Weyl scalar, \psi_0 . We use a mode-sum renormalization and
find the renormalization coefficients by matching a series in L = \ell + 1/2 to
the large-L behavior of the expression for the self-force in terms of the
retarded field h_{\alpha\beta}^{ret}; we similarly find the leading
renormalization coefficients of h_{uu} and the related change in the angular
velocity of the particle due to its self-force. We show numerically that the
singular part of the self-force has the form f_{\alpha} \propto < \nabla_\alpha
\rho^{-1}>, the part of \nabla_\alpha \rho^{-1} that is axisymmetric about a
radial line through the particle. This differs only by a constant from its form
for a Lorenz gauge. It is because we do not use a radiation gauge to describe
the change in black-hole mass that the singular part of the self-force has no
singularity along a radial line through the particle and, at least in this
example, is spherically symmetric to subleading order in \rho.