Spacetimes containing slowly evolving horizons

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.

Figure 1

The evolution of an initially solar mass black hole as dust shells of various masses collapse onto it. The bottom part of this graph shows the corresponding values of the slowly evolving parameter. It is clear that while all of the MTTs start and finish as slowly evolving, for larger mass shells they are not always slowly evolving throughout their evolution.

Figure 2

The collapse of dust clouds of various initial masses to form a black hole. The bottom part of this graph shows the corresponding values of the slowly evolving parameter. While in all of the cases the MTTs asymptote into SEHs, note that for $\mu =0.25$ the horizon is slowly evolving throughout its formation and evolution.