Causality and hyperbolicity of Lovelock theories

Harvey S. Reall, Norihiro Tanahashi, Benson Way

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)


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.

Original languageEnglish
Article number205005
JournalClassical and Quantum Gravity
Issue number20
Publication statusPublished - Oct 21 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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