Black hole spacetimes
Wednesday, June 26, 2002 - 9:00am - 9:50am
Jeff Winicour (University of Pittsburgh)
I describe the properties of the the horizon of an observer and the event horizon of a black hole spacetime, with emphasis on those aspects important for numerical simulation. The boundary of the spacetime region which can causally effect a given spacetime point P constitutes the event horizon of the observer at P. Thus the horizon is determined by the maximum signal propagation speed, i.e. by the characteristics of the partial differential equations underlying the theory. In relativity, these are the light rays. A black hole event horizon is the boundary of the causal past of the collection of observers at all distant spacetime points. In the flat spacetime of special relativity this boundary is empty and there are no black holes. In the curved spacetime of general relativity, black holes are produced by the lensing effect of a body undergoing gravitational collapse to a singularity. The final singularity is an impediment to numerical simulation. Fortunately, theoretical arguments suggest that the singularity lies inside the black hole and does not affect observations by distant astronomers. This allows singularity-avoiding strategies for computing the gravitational radiation emitted in the formation of black holes. This has been achieved with some success for a single black hole. Current efforts concentrate on handling the inspiral and merger of a binary black hole, which has a more complicated horizon structure.