Exact analytic characteristic initial data for axisymmetric, non-rotating, vacuum spacetimes, with an application to the binary black hole problem

Details Exact analytic characteristic initial data for axisymmetric, non-rotating, vacuum spacetimes, with an application to the binary black hole problem Exact analytic characteristic initial data for axisymmetric, non-rotating, vacuum spacetimes, with an application to the binary black hole problem

1998-11-21

arxiv.org/abs/gr-qc/9811074v1

Class.Quant.Grav. 15 (1998) 2509-2522

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages. Published in Class. Quantum Grav. 15, 2509-2522

Scientific paper

10.1088/0264-9381/15/8/025

Bondi's approach to the construction of a coordinate system is used with a different choice of gauge, in accordance with which the radial coordinate r is an affine parameter, to cast the metric tensor into a form suitable for use with the Newman-Penrose null tetrad formalism. The choice of tetrad has the result that the equations and all the functions that appear in them are real-valued. A group classification of the Sachs equations in this gauge leads to a unique expression for the first of the five independent elements $\Psi_0$ of the Weyl spinor, and to the corresponding exact solutions for two of the metric functions on an initial null hypersurface. A proof is presented that the result for $\Psi_0$ constitutes the appropriate characteristic initial value function for all physically realistic axisymmetric, non-rotating vacuum spacetimes. Integration of the field equations on the axis of symmetry when an equatorial symmetry plane is also present, and on the equatorial plane itself when time rates of change can be neglected, shows that these data produce results consistent with Newton's laws and with the Schwarzschild solution in the appropriate limits. The solution on the axis of symmetry indicates that the Weyl curvature increases without limit between black holes as their separation decreases.

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