How trapped surfaces jump in 2 + 1 dimensions

Abstract

When a lump of matter falls into a black hole it is expected that a marginally trapped tube when hit moves outwards everywhere, even in regions not yet in causal contact with the infalling matter. But to describe this phenomenon analytically in 3+1 dimensions is difficult since gravitational radiation is emitted. By considering a particle falling into a toy model of a black hole in 2+1 dimensions an exact description of this non-local behaviour of a marginally trapped tube is found.

Symmetry and instability of marginally outer trapped surfaces

“…Pairs can also annihilate. These behaviors have been much discussed over the years (see, for example, [2,3,9,28,44]), seen in binary mergers (for example [18,21,42,44,45]) and in exact solutions (for example [7,9,27]). In all observed cases, the MOTS that appears (disappears) in a creation (annihilation) event has a vanishing eigenvalue of L S (though not necessarily λ 1 ).…”

Some Examples of Trapped Surfaces

“…Now suppose we start with a single BTZ black hole, choose a radial null geodesic leaving J and heading for the event horizon, choose a suitable wedge with that geodesic as its edge, and identify the two boundaries of the wedge using an element of the isometry group. This then describes a lump of matter falling into a black hole, and the question arises how it will affect the black hole when it hits [26].…”

“…In section 4 we restrict ourselves to a 2+1 dimensional toy model of gravity (with a negative cosmological constant) [21,22,23,24], where a complete description of all marginally trapped "surfaces" in spacetime can be had [25]. In this toy model we will also see how the trapped surfaces "jump" when we throw lumps of matter into a black hole [26], and-by increasing the dimension again-what a dynamical horizon can look like in the vacuum case [27].…”

“…d) The identification surfaces meet in a singular point at infinity. Reproduced with permission[26].…”