Causality and hyperbolicity of Lovelock theories
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Publication:2936430
DOI10.1088/0264-9381/31/20/205005zbMATH Open1304.83013arXiv1406.3379OpenAlexW2004231062WikidataQ125932856 ScholiaQ125932856MaRDI QIDQ2936430
Author name not available (Why is that?)
Publication date: 16 December 2014
Published in: (Search for Journal in Brave)
Abstract: In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalise 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.
Full work available at URL: https://arxiv.org/abs/1406.3379
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