Arxiv:2006.03939V1 [Gr-Qc] 6 Jun 2020 in flat Spacetime Regions
Horizons in a binary black hole merger I: Geometry and area increase Daniel Pook-Kolb,1, 2 Ofek Birnholtz,3 Jos´eLuis Jaramillo,4 Badri Krishnan,1, 2 and Erik Schnetter5, 6, 7 1Max-Planck-Institut f¨urGravitationsphysik (Albert Einstein Institute), Callinstr. 38, 30167 Hannover, Germany 2Leibniz Universit¨atHannover, 30167 Hannover, Germany 3Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel 4Institut de Math´ematiquesde Bourgogne (IMB), UMR 5584, CNRS, Universit´ede Bourgogne Franche-Comt´e,F-21000 Dijon, France 5Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada 6Physics & Astronomy Department, University of Waterloo, Waterloo, ON N2L 3G1, Canada 7Center for Computation & Technology, Louisiana State University, Baton Rouge, LA 70803, USA Recent advances in numerical relativity have revealed how marginally trapped surfaces behave when black holes merge. It is now known that interesting topological features emerge during the merger, and marginally trapped surfaces can have self-intersections. This paper presents the most detailed study yet of the physical and geometric aspects of this scenario. For the case of a head-on collision of non-spinning black holes, we study in detail the world tube formed by the evolution of marginally trapped surfaces. In the first of this two-part study, we focus on geometrical properties of the dynamical horizons, i.e. the world tube traced out by the time evolution of marginally outer trapped surfaces. We show that even the simple case of a head-on collision of non-spinning black holes contains a rich variety of geometric and topological properties and is generally more complex than considered previously in the literature.
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