It is well known that quasilocal black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasilocal physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on nonspherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that, as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order 0.017% for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasilocal horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.

• Received 13 August 2010

DOI:https://doi.org/10.1103/PhysRevD.83.124022