Metric of a tidally perturbed spinning black hole

Journal Article · Sun Jan 15 00:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.73.0· OSTI ID:20795727

Yunes, Nicolas ^[1]; Gonzalez, Jose A ^[2]

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1. Institute for Gravitational Physics and Geometry, Center for Gravitational Wave Physics, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802-6300 (United States)
2. Theoretical Physics Institute, University of Jena, Max-Wien-Platz 1, 07743, Jena (Germany)

We explicitly construct the metric of a Kerr black hole that is tidally perturbed by the external universe in the slow-motion approximation. This approximation assumes that the external universe changes slowly relative to the rotation rate of the hole, thus allowing the parameterization of the Newman-Penrose scalar {psi}{sub 0} by time-dependent electric and magnetic tidal tensors. This approximation, however, does not constrain how big the spin of the background hole can be and, in principle, the perturbed metric can model rapidly spinning holes. We first generate a potential by acting with a differential operator on {psi}{sub 0}. From this potential we arrive at the metric perturbation by use of the Chrzanowski procedure in the ingoing radiation gauge. We provide explicit analytic formulas for this metric perturbation in Kerr coordinates, where the perturbation is finite at the horizon. This perturbation is parametrized by the mass and Kerr spin parameter of the background hole together with the electric and magnetic tidal tensors that describe the time evolution of the perturbation produced by the external universe. In order to make the metric accurate far away from the hole, these tidal tensors should be determined by asymptotically matching this metric to another one valid far from the hole. The tidally perturbed metric constructed here could be useful in initial data constructions to describe the metric near the horizons of a binary system of spinning holes. This perturbed metric could also be used to construct waveforms and study the absorption of mass and angular momentum by a Kerr black hole when external processes generate gravitational radiation.

• OSTI ID: 20795727
• Journal Information: Physical Review. D, Particles Fields, Vol. 73, Issue 2; Other Information: DOI: 10.1103/PhysRevD.73.024010; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ABSORPTION
APPROXIMATIONS
BLACK HOLES
COSMOLOGY
DISTURBANCES
GENERAL RELATIVITY THEORY
GRAVITATIONAL RADIATION
GRAVITATIONAL WAVE DETECTORS
GRAVITATIONAL WAVES
MASS
METRICS
POTENTIALS
ROTATION
SCALARS
SPACE-TIME
SPIN
TENSORS
TIME DEPENDENCE
UNIVERSE
WAVE FORMS