Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 31, Issue 20, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/31/20/205005
Keywords
Gauss-Bonnet gravity; Lovelock gravity; higher curvature gravity
Categories
Funding
- European Research Council [ERC-2011-StG 279363-HiDGR]
- World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan
- JSPS [25.755]
- Science and Technology Facilities Council [ST/L000636/1, ST/L000385/1] Funding Source: researchfish
- STFC [ST/L000385/1, ST/L000636/1] Funding Source: UKRI
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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.
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