Marginally outer trapped surfaces in the maximal Kruskal-Szekeres extension

Abstract

For the last few decades and especially since the first detection of gravitational waves, black hole mergers have been a core research area in general relativity. However, the process by which two black hole horizons merge is only now starting to be wellunderstood. In numerical studies of apparent horizon evolution, self-intersecting marginally outer-trapped surfaces (MOTS) were found and play a key role [12]. Later a seemingly infinite number of self-intersectingMOTSs were found in Painlev´e–Gullstrand slices of the Schwarzschild solution [4]. Further work has shown that their existence is robust and not simply an artifact of that coordinate system [11]. This thesis presents results found when examining the maximal extension to the Schwarzschild black hole in Kruskal-Szekeres coordinates. In this system, two separate universes dynamically connect through a worm-hole and pass through a moment of time-symmetry before the worm-hole pinches off and they disconnect. In these time slices, self-intersecting MOTS are found which, among other things, straddle the Einstein-Rosen bridge extending into both universes. Of particular interest is the stability analysis of the numerical solvers used, exotic toroidal surfaces, and the MOTS stability operator.