This raises a point about solutions of Einstein's equations which we have not yet mentioned. When constructing solutions of Einstein's initial-value equations, we are free to specify the topology of the initial-data hypersurface. Einstein's equations of general relativity place no constraints on the topology of the spacetime they describe or of spacelike hypersurfaces that foliate it. For astrophysical black holes (i. e., black holes in an asymptotically flat spacetime), the freedom in the choice of the topology has relatively minor consequences. The primary effects of different topology choices are hidden within the black hole's event horizon.
In the sections below, we will explore many of the existing black-hole solutions and the schemes for generating them.
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Initial Data for Numerical Relativity
Gregory B. Cook http://www.livingreviews.org/lrr-2000-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |