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Published October 15, 2005 | public
Journal Article Open

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

Mandel, Ilya


The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holes into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a "radiation-reaction field." (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves—sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.

Additional Information

© 2005 The American Physical Society. Received 30 May 2005; published 25 October 2005. I am very grateful to my advisor, Kip S. Thorne, for posing this research project and for his extremely patient guidance. Jonathan Gair, Lee Lindblom, Robert Owen, Frans Pretorius and Mark A. Scheel of the TAPIR group at Caltech made many helpful suggestions, as did Ronald J. Adler and Alexander S. Silbergleit of the GP-B theory seminar at Stanford, and Richard Price of UT Brownsville. I was partially supported by NSF Grant No. PHY-0099568 and NASA Grant No. NAG5-12834.


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August 22, 2023
August 22, 2023