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 nonnull 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 nonnull. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a wellposed problem.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 October 2014
 DOI:
 10.1088/02649381/31/20/205005
 arXiv:
 arXiv:1406.3379
 Bibcode:
 2014CQGra..31t5005R
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 33 pages, v2 added references