No-hair theorems for noncanonical self-gravitating static multiple scalar fields
Abstract
We prove under certain assumptions no-hair theorems for noncanonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multiscalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann boundary conditions cannot support a nontrivial self-gravitating noncanonical (and canonical) multiscalar map in their exterior spacetime regions. In order to prove the no-hair theorems we derive a new divergence identity.
- Publication:
-
Physical Review D
- Pub Date:
- October 2020
- DOI:
- 10.1103/PhysRevD.102.084055
- arXiv:
- arXiv:2008.01965
- Bibcode:
- 2020PhRvD.102h4055D
- Keywords:
-
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 7 pages