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Gravitational radiation from a particle in circular orbit around a black hole. III. Stability of circular orbits under radiation reaction

Apostolatos, Theocharis and Kennefick, Daniel and Ori, Amos and Poisson, Eric (1993) Gravitational radiation from a particle in circular orbit around a black hole. III. Stability of circular orbits under radiation reaction. Physical Review D, 47 (12). pp. 5376-5388. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:APOprd93

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Abstract

We use the Teukolsky perturbation formalism to show that (i) a particle in circular motion around a nonrotating black hole remains in a circular orbit under the influence of radiation reaction, and (ii) circular orbits are stable only if the orbital radius is greater than a critical radius rc -~ 6.6792M, where M is the mass of the black hole. A circular orbit is stable if, when slightly perturbed so that it acquires a small eccentricity, the radiation reaction decreases the eccentricity; a circular orbit is unstable if the radiation reaction increases the eccentricity. Our analysis is restricted by four major assumptions: (i) the black hole is nonrotating, (ii) the eccentricity is always small, (iii) the gravitational perturbations are linear, and (iv) the adiabatic approximation (that the radiation reaction takes place over a time scale much larger than the orbital period) is valid. On the other hand, our analysis is not limited to weak-field, slow-motion situations; it is valid for particle motion in strong gravitational fields.


Item Type:Article
Additional Information:©1993 The American Physical Society. Received 10 February 1993. For numerous discussions we thank Kip Thorne and the members of the Relativity Group at Caltech. We also thank George Djorgovski for the use of his computing facilities and Julia Smith for much computing help and advice. The work presented here was supported by NSF Grant No. AST 9114925 and NASA Grant No. NAGW-2897. Eric Poisson acknowledges support from the Natural Sciences and Engineering Research Council of Canada.
Subject Keywords:PERTURBATIONS
Record Number:CaltechAUTHORS:APOprd93
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:APOprd93
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.47.5376
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6723
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Dec 2006
Last Modified:26 Dec 2012 09:24

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