Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture
Abstract
A dynamically transversely trapping surface (DTTS) is a new concept for an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.
- Publication:
-
Progress of Theoretical and Experimental Physics
- Pub Date:
- May 2020
- DOI:
- 10.1093/ptep/ptaa050
- arXiv:
- arXiv:1911.09893
- Bibcode:
- 2020PTEP.2020e3E01Y
- Keywords:
-
- E31;
- E00;
- A13;
- General Relativity and Quantum Cosmology;
- Astrophysics - Astrophysics of Galaxies
- E-Print:
- 24 pages, 15 figures, minor corrections, published version