Toroidal horizons in binary black hole mergers

Creators: Bohn, Andy; Kidder, Lawrence E.; Teukolsky, Saul A.

Abstract

We find the first binary black hole event horizon with a toroidal topology. It has been predicted that generically the event horizons of merging black holes should briefly have a toroidal topology. However, such a phase has never been seen in numerical simulations. Instead, in all previous simulations, the topology of the event horizon transitions directly from two spheres during the inspiral to a single sphere as the black holes merge. We find a coordinate transformation to a foliation of spacelike hypersurfaces that "cut a hole" through the event horizon surface, resulting in a toroidal event horizon, thus reconciling the numerical work with theoretical expectations. The demonstration requires extremely high numerical precision, which is made possible by a new event horizon code described in a companion paper. A torus could potentially provide a mechanism for violating topological censorship. However, these toroidal event horizons satisfy topological censorship by construction, because we can always trivially apply the inverse coordinate transformation to remove the topological feature.

Additional Information

© 2016 American Physical Society. (Received 7 June 2016; published 2 September 2016) We thank Aaron Zimmerman for the suggestion of using a negative amplitude Gaussian to create a baby event horizon and for helpful dialogue regarding topologies of event horizon surfaces. For ongoing feedback and suggestions for finding toroidal event horizons over the past few years, we thank Jeffrey Winicour. We also thank Michael Boyle for useful conversations about topologies of event horizon surfaces and useful paper comments. We thank Leo C. Stein for verifying the effects of coordinate transformations and useful paper comments. For keeping the SpEC code from changing under us while we were locating event horizons, we thank Daniel A. Hemberger. We are grateful to Jordan Moxon, Nils Deppe, and François Hébert for time slicing conversations and useful comments during the editing phase of this paper. We also thank Harald Pfeiffer for providing the BBH simulation with parameters similar to the system detected by Advanced LIGO. For helping smooth the visualization of event horizon surfaces, we thank Curran D. Muhlberger. We gratefully acknowledge support for this research at Cornell from the Sherman Fairchild Foundation and NSF Grants No. PHY-1306125 and No. AST-1333129. Calculations were performed on the Zwicky cluster at Caltech, which is supported by the Sherman Fairchild Foundation and by NSF Grant No. PHY-0960291; on the NFS XSEDE network under Grant No. TG-PHY990007N; at the GPC supercomputer at the SciNet HPC Consortium [36]. SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada, the Government of Ontario, Ontario Research Fund Research Excellence, and the University of Toronto. All the surface visualizations were done using Paraview [37]. The line plots were produced using the Matplotlib [38] library with Python.

Attached Files

Published - PhysRevD.94.064009.pdf

Submitted - 1606.00436

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PhysRevD.94.064009.pdf

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