Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a radiation gauge

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.064018· OSTI ID:21537538

Shah, Abhay G; Friedman, John L; Price, Larry R ^[1]; Keidl, Tobias S ^[2]; Kim, Dong-Hoon ^[3]

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1. Center for Gravitation and Cosmology, Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201 (United States)
2. Department of Physics, University of Wisconsin-Washington County (United States)
3. Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany)

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. In a test of the method delineated in the first paper, 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{sub {alpha}{beta}u}{sup {alpha}u{beta}} must have the same value for our radiation gauge as for a Lorenz gauge; and we confirm this numerically to one part in 10{sup 14}. As outlined in the first paper, the perturbed metric is constructed from a Hertz potential that is in a term obtained algebraically from the retarded perturbed spin-2 Weyl scalar, {psi}{sub 0}{sup ret}. We use a mode-sum renormalization and find the renormalization coefficients by matching a series in L=l+1/2 to the large-L behavior of the expression for the self-force in terms of the retarded field h{sub {alpha}{beta}}{sup ret}; we similarly find the leading renormalization coefficients of h{sub {alpha}{beta}u}{sup {alpha}u{beta}} 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{sub {alpha}}{sup S}=<{nabla}{sub {alpha}{rho}}{sup -1}>, the part of {nabla}{sub {alpha}{rho}}{sup -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}.

• OSTI ID: 21537538
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevD.83.064018; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR VELOCITY
AXIAL SYMMETRY
BLACK HOLES
CENTER-OF-MASS SYSTEM
COMPUTERIZED SIMULATION
DISTURBANCES
GAUGE INVARIANCE
LORENTZ INVARIANCE
MASS
ORBITS
PERTURBATION THEORY
RENORMALIZATION
SCHWARZSCHILD METRIC
SINGULARITY
SPIN
ANGULAR MOMENTUM
INVARIANCE PRINCIPLES
METRICS
PARTICLE PROPERTIES
SIMULATION
SYMMETRY
VELOCITY