Nonrotating black hole in a post-Newtonian tidal environment
- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)
We examine the motion and tidal dynamics of a nonrotating black hole placed within a post-Newtonian external spacetime. The black hole's gravity is described accurately to all orders in Gm/c{sup 2}r, where m is the black-hole mass and r is the distance to the black hole. The tidal perturbation created by the external environment is treated as a small perturbation. At a large distance from the black hole, the gravitational field of the external distribution of matter is assumed to be sufficiently weak to be adequately described by the (first) post-Newtonian approximation to general relativity. There, the black hole is treated as a monopole contribution to the total gravitational field. There exists an overlap in the domains of validity of each description, and the black-hole and post-Newtonian metrics are matched in the overlap. The matching procedure produces (i) a justification of the statement that a nonrotating black hole is a post-Newtonian monopole; (ii) a complete characterization of the coordinate transformation between the inertial, barycentric frame and the accelerated, black-hole frame; (iii) the equations of motion for the black hole; and (iv) the gravito-electric and gravito-magnetic tidal fields acting on the black hole. We first calculate the equations of motion and tidal fields by making no assumptions regarding the nature of the post-Newtonian environment; this could contain a continuous distribution of matter (so as to model a galactic core) or any number of condensed bodies. We next specialize our discussion to a situation in which the black hole is a member of a post-Newtonian two-body system. As an application of our results, we examine the geometry of the deformed event horizon and calculate the tidal heating of the black hole, the rate at which it acquires mass as a result of its tidal interaction with the companion body.
- OSTI ID:
- 21254441
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 78, Issue 8; Other Information: DOI: 10.1103/PhysRevD.78.084016; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COSMOLOGY AND ASTRONOMY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BLACK HOLES
COORDINATES
DISTANCE
DISTRIBUTION
DISTURBANCES
EQUATIONS OF MOTION
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL FIELDS
INTERACTIONS
MASS
MONOPOLES
PERTURBATION THEORY
SPACE-TIME
TRANSFORMATIONS
TWO-BODY PROBLEM