Causality and hyperbolicity of Lovelock theories
Abstract
In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalize a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- October 2014
- DOI:
- 10.1088/0264-9381/31/20/205005
- arXiv:
- arXiv:1406.3379
- Bibcode:
- 2014CQGra..31t5005R
- Keywords:
-
- Gauss-Bonnet gravity;
- Lovelock gravity;
- higher curvature gravity;
- 04.50.-h;
- 04.20.-q;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 33 pages, v2 added references