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Title: Binary black hole spacetimes with a helical Killing vector

Abstract

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metricmore » functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.« less

Authors:
 [1]
  1. Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Inselstrasse 22, 04103, Leipzig (Germany)
Publication Date:
OSTI Identifier:
20698264
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 70; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.70.124026; (c) 2004 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; AXIOMATIC FIELD THEORY; BLACK HOLES; COSMOLOGY; EINSTEIN FIELD EQUATIONS; GRAVITATION; GRAVITATIONAL WAVES; MATHEMATICAL SOLUTIONS; MULTIPOLES; NONLINEAR PROBLEMS; SIGMA MODEL; SINGULARITY; SO GROUPS; SPACE-TIME; TOPOLOGY; VECTORS

Citation Formats

Klein, Christian. Binary black hole spacetimes with a helical Killing vector. United States: N. p., 2004. Web. doi:10.1103/PhysRevD.70.124026.
Klein, Christian. Binary black hole spacetimes with a helical Killing vector. United States. https://doi.org/10.1103/PhysRevD.70.124026
Klein, Christian. 2004. "Binary black hole spacetimes with a helical Killing vector". United States. https://doi.org/10.1103/PhysRevD.70.124026.
@article{osti_20698264,
title = {Binary black hole spacetimes with a helical Killing vector},
author = {Klein, Christian},
abstractNote = {Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.},
doi = {10.1103/PhysRevD.70.124026},
url = {https://www.osti.gov/biblio/20698264}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 70,
place = {United States},
year = {Wed Dec 15 00:00:00 EST 2004},
month = {Wed Dec 15 00:00:00 EST 2004}
}