Closest safe approach to an accreting black hole

Abstract

We examine the causal and geometric horizons of dynamical black holes in Lemaitre-Tolman-Bondi collapsing dust spacetimes. Marginally trapped tubes in these spacetimes may be spacelike, timelike or null and may also be sourced from or disappear into shell-crossing singularities which we resolve with (timelike) shockwaves. The event horizon kinks when it intersects a shockwave. We calculate the timelike separation between the crossable boundary (marginally trapped tubes plus connecting shockwaves) and event horizon. As measured along the crossable boundary this function can have discontinuities not only in its derivative but also in the function itself. These features are closely related to the geometry of the crossable boundary. Finally, we consider the application of this work for future space explorers seeking to make a closest (non-terminal) approach to a black hole horizon.

Evolutions from extremality

“…Again this isn't usually seen for marginally trapped tubes which may weave backwards and forwards through spacetime but do not generally appear out of nowhere. During gravitational collapse they may appear out of the central singularity as it forms and there are known examples of them forming out of or disappearing into shockwave singularities [41] however as far as we know this kind of appearance "from thin air" has not be commented on before. Once more the strangely behaving horizon is extremal and so not subject to the usual theorems for strictly stably outermost horizons.…”

“…Note however that this stress is strangely innocuous. By (40), (41), (64) and (63) the bulk part of the stressenergy tensor is continuous across the MTT: there are no lasting jumps in either energy, momentum or stress density. This may seem surprising given the appearance of FIG.…”