Slicing dependence of nonspherically symmetric quasilocal horizons in Vaidya spacetimes

Abstract

It is well known that quasi-local 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 quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically 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 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 withṁ = 0.02. We also calculate analytically the difference in area between the spherically symmetric quasi-local 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.

Trapped Surfaces

“…In conjunction with the nonuniqueness of dynamical horizons, this poses a fundamental puzzle for the physics of black holes. Four possible solutions have been put forward 6,10,11,19,31,34 :…”

Revisiting Vaidya Horizons

“…The problems with marginally outer trapped surfaces and trapping horizons have also been examined. They are non-unique, depending on a choice of foliation [9], or equivalently a choice of null normals, they may intersect a given spatial hypersurface multiple times [1], they may extend partially into flat space regions [15], they have difficulties with the generalised second law [16] and are not invariant under conformal transformations [17].…”

“…A detailed discussion of the difference between the event horizon and the marginally trapped tubes of the Vaidya solution can be found in [8]. A collection of useful results relating to the Vaidya solution can be found amongst other places in [9].…”

Conformally rescaled spacetimes and Hawking radiation

“…Spherical symmetry has many practical advantages, a chief one being that the surfaces of spherical isometry define a natural slicing of the quasi-local horizons and so in turn select out "preferred" quasi-local horizons. This is despite the fact that even in spherical symmetry there exist many different intersecting quasi-local horizons [23]. We will ignore these and other technical issues in this work by focusing purely on spherically symmetric horizons.…”