Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.084010· OSTI ID:21432380

Hopper, Seth; Evans, Charles R ^[1]

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1. Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599 (United States)

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle source terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of r traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity C{sup -1} typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.

• OSTI ID: 21432380
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 8; Other Information: DOI: 10.1103/PhysRevD.82.084010; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANGULAR MOMENTUM
BLACK HOLES
COMPUTERIZED SIMULATION
DELTA FUNCTION
DISTRIBUTION
GAUGE INVARIANCE
GRAVITATION
MASS
MATHEMATICAL SOLUTIONS
METRICS
PERTURBATION THEORY
SCHWARZSCHILD RADIUS
SPHERICAL CONFIGURATION
TIME DEPENDENCE
TRANSFORMATIONS
WAVE EQUATIONS
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INVARIANCE PRINCIPLES
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION