Foliation dependence of black hole apparent horizons in spherical symmetry

Abstract

International audienceNumerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples

Embedding Black Holes and Other Inhomogeneities in the Universe in Various Theories of Gravity: A Short Review

“…This problem is alleviated (or, for purely practical purposes, largely eliminated), but not solved, in spherical symmetry. In this case, the apparent horizons coincide in all spherical foliations [51].…”

Geometric horizons in the Kastor-Traschen multi-black-hole solutions

“…In general, GHs will not be apparent horizons, dynamical horizons or MTTs. However, for spherically symmetric dynamical black hole solutions GHs will coincide with the unique dynamical horizon r = 2M [23,17]. Furthermore, if a dynamical black hole solution settles down to a dynamical solution where the black hole is no longer interacting with the exterior region, then the GHs will coincide with IHs [7,1].…”

“…where r is the areal radius, will detect the unique, invariantly defined dynamical horizon r = 2M [23]. For the spherically symmetric dynamical black holes and dynamical black holes conformally related to stationary black holes the GHs correspond to MTTs.…”

“…Similarly, we will say any GH for which θ (− ) < 0 in all GOTSs is a dynamical GH. If a dynamical black hole solution asymptotically evolves to a spherically symmetric dynamical black hole, the dynamical GH will correspond to the dynamical horizon [23,17].…”

An invariant characterization of the quasi-spherical Szekeres dust models

“…The QS Szekeres dust models admit an apparent horizon, defined by the surface R = 2M , which corresponds to the vanishing expansion of the future-pointing null vector normal to this surface [16]. Due to the lack of a timelike Killing vector or spherical symmetry, there are no previously known scalar polynomial curvature invariants (SPIs) that will, in general, detect the apparent horizon [39,40].…”