

Preprint 74/2004
Binary black hole spacetimes with a helical Killing vector
Christian Klein
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Submission date: 27. Oct. 2004
Pages: 27
published in: Physical review / D, 70 (2004) 12, art-no. 124026
DOI number (of the published article): 10.1103/PhysRevD.70.124026
Bibtex
PACS-Numbers: 04.70.Bw, 04.03.Db
Keywords and phrases: binary black holes
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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 sigma model as
the material source. The
sigma model is determined by a complex Ernst equation. 2+1 decompositions
of the
3-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 non-axisymmetric setting, the asymptotic multipoles are not defined. The asymptotic
behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.