Spacetimes containing slowly evolving horizons

Abstract

Slowly evolving horizons are trapping horizons that are "almost" isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes.

Isolated, slowly evolving, and dynamical trapping horizons: Geometry and mechanics from surface deformations

“…If this is the case, the two results will agree as we can set A = 1 + O(ǫ). However, there does not seem to be any analytic justification for this, and the examples of slowly evolving horizons studied so far in [27] are all (approximately) spherically symmetric, whence A is automatically (approximately) constant by construction. Thus, whether or not this assumption holds is currently an open question.…”

“…As such, this idea of studying the "boundary" of a trapped region without first finding a corresponding bulk has become increasingly popular in the last few years. Apart from the further studies of trapping horizons [8,9] there are closely related programmes such as isolated horizons which identify and study equilibrium states [10][11][12][13][14], dynamical horizons which correspond to non-trivially evolving horizons [15][16][17][18][19][20][21][22][23][24][25], and slowly evolving horizons which are "almost isolated" trapping horizons [26,27]. For reviews of the field see, for example [28][29][30].…”

Extremality conditions for isolated and dynamical horizons

“…For isolated horizons these arise from (1) the non-negativity of the surface gravity and (2) the idea that there should be trapped surfaces just inside the horizon. For dynamical horizons only the second these characterizations is appli-cable since the surface gravity is only meaningful for slowly evolving dynamical horizons (in the sense of [19][20][21]). …”

Black holes and black hole thermodynamics without event horizons

“…The event horizon would be close to a Killing horizon, but not exactly so. In fact, it is likely that the vast majority of astrophysical blacks are described by some sort of slowly evolving horizon [68], rather than an exact Killing horizon.…”

“…Using slightly different definitions, perturbative deviations from spherical symmetry were considered in [68].…”