Time-asymmetric initial data for black holes and black-hole collisions
- 15 April 1980
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 21 (8), 2047-2056
- https://doi.org/10.1103/physrevd.21.2047
Abstract
As a first step in constructing initial data for dynamic black holes and general black-hole collisions, we study nonsingular vacuum Cauchy hypersurfaces with two isometric asymptotically flat ends connected by an Einstein-Rosen-type bridge. These hypersurfaces are assumed to be conformally flat and maximally embedded in spacetime but are neither spherically symmetric nor time symmetric. Three of the four constraints are solved explicitly for suitable extrinsic curvature tensors that possess linear momentum and/or intrinsic angular momentum. The complete initial data are shown to transform invariantly, modulo the sign of the extrinsic curvature tensor, under inversion through a minimal two-surface that represents the "throat" of the geometry. These and other properties show that the data represent a particular epoch in the history of a dynamic black hole. We describe the relation of our data to that of the Schwarzschild and Kerr balck holes. Finally, we discuss the generalization to encounters of two or more black holes.Keywords
This publication has 16 references indexed in Scilit:
- General form for the longitudinal momentum of a spherically symmetric sourceGeneral Relativity and Gravitation, 1979
- Time functions in numerical relativity: Marginally bound dust collapsePhysical Review D, 1979
- Kinematical conditions in the construction of spacetimePhysical Review D, 1978
- Evolution of time-symmetric gravitational waves: Initial data and apparent horizonsPhysical Review D, 1977
- Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativityJournal of Mathematical Physics, 1973
- Initial-Value Problem on Einstein-Rosen ManifoldsJournal of Mathematical Physics, 1963
- Interaction Energy in GeometrostaticsPhysical Review B, 1963
- Wormhole Initial ConditionsPhysical Review B, 1960
- On the positive definite mass of the Bondi-Weber-Wheeler time-symmetric gravitational wavesAnnals of Physics, 1959
- Classical physics as geometryAnnals of Physics, 1957