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

Abstract

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 modelmore » 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.« less

Authors:
 [1]
  1. Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125 (United States)
Publication Date:
OSTI Identifier:
20713746
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 72; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.72.084025; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCURACY; BLACK HOLES; COSMOLOGY; ENERGY DENSITY; GEOMETRY; GRAVITATIONAL WAVES; SCALAR FIELDS; SCHWARZSCHILD METRIC; SINGULARITY; SPACE-TIME; STANDING WAVES; VECTOR FIELDS

Citation Formats

Mandel, Ilya. Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.084025.
Mandel, Ilya. Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem. United States. https://doi.org/10.1103/PhysRevD.72.084025
Mandel, Ilya. 2005. "Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem". United States. https://doi.org/10.1103/PhysRevD.72.084025.
@article{osti_20713746,
title = {Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem},
author = {Mandel, Ilya},
abstractNote = {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.},
doi = {10.1103/PhysRevD.72.084025},
url = {https://www.osti.gov/biblio/20713746}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 72,
place = {United States},
year = {Sat Oct 15 00:00:00 EDT 2005},
month = {Sat Oct 15 00:00:00 EDT 2005}
}