Horizon boundary condition for black hole spacetimes

Peter Anninos, Greg Daues, Joan Massó, Edward Seidel, Wai Mo Suen

Research output: Contribution to journalArticlepeer-review


It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this scheme. The scheme is based on using (1) a horizon-locking coordinate which locks the coordinate system to the geometry and (2) a finite differencing scheme which respects the causal structure of the spacetime. We show that the horizon-locking coordinate can be affected by a number of shift conditions, such as, a ''distance freezing'' shift, an ''area freezing'' shift, an ''expansion freezing'' shift, or the minimal distortion shift. The causal differencing scheme is illustrated with the evolution of scalar fields, and its use in evolving the Einstein equations is studied. We compare the results of numerical evolutions with and without the use of this horizon boundary condition scheme for spherical black hole spacetimes. With this boundary condition a black hole can be evolved accurately well beyond t=1000M, where M is the black hole mass.

Original languageEnglish (US)
Pages (from-to)5562-5578
Number of pages17
JournalPhysical Review D
Issue number10
StatePublished - 1995

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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