Evolving Black Hole Horizons in General Relativity and Alternative Gravity

Abstract

From the microscopic point of view, realistic black holes are time-dependent and the teleological concept of the event horizon fails. At present, the apparent or trapping horizon seem to be its best replacements in various areas of black hole physics. We discuss the known phenomenology of apparent and trapping horizons for analytical solutions of General Relativity and alternative theories of gravity. These specific examples (we focus on spherically symmetric inhomogeneities in a background cosmological spacetime) are useful as toy models for research on various aspects of black hole physics

Evolving Hořava cosmological horizons

“…Also since the congruences are supposed to be null, l ↑ a l ↑ a = l ↓ a l ↓ a = 0. Accordingly, the congruence expansion for outgoing and ingoing congruence on the so-called transverse surface would be [36] …”

“…The apparent horizons can be regarded also as trapping horizons if the foliating 2-spheres of symmetry satisfy conditions on the Lie derivative L ↑ Θ ↓ [36]. According to Eqs.…”

“…To do this we take two null congruences corresponding to outgoing and ingoing trajectories. Letting g ab be the background spacetime metric, we can then generate these congruences by the tangential vector fields l ↑ and l ↓ , which constitute a transverse 2-surface described by the 2-metric [36] …”

Lemaître model and cosmic mass

“…There are strong claims in the literature that, in the absence of a preferred time derived from a timelike Killing vector, the Kodama vector introduces a preferred time and surface gravity on apparent horizons, which determine a Hawking temperature and make thermodynamics meaningful for timeevolving apparent horizons (see Ref. [33][34][35] for reviews). Given the geometry (2.4), the Kodama vector is [19] (3.4) and, in the Lemaître geometry (2.10), it has components…”

Inhomogeneities in Cosmological “Backgrounds” in Einstein Theory

“…Explicit analytic expressions for the apparent horizon radii are rare to find in studies of time-evolving black holes [49].…”