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 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.

33 pages, v2 added references

References in corpus (12)

• Viscosity Bound and Causality Violation
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• (In)stability of D-dimensional black holes in Gauss-Bonnet theory
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Catastrophic Instability of Small Lovelock Black Holes
• Lovelock theories, holography and the fate of the viscosity bound
• Causal Structures in Gauss-Bonnet gravity
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
• Stability of Lovelock Black Holes under Tensor Perturbations
• Spherical collapse of inhomogeneous dust cloud in the Lovelock theory

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• 4D Einstein-Lovelock black holes: Hierarchy of orders in curvature
• Shock Formation in Lovelock Theories
• Well-posedness of cubic Horndeski theories
• Holographic constraints on Bjorken hydrodynamics at finite coupling
• Local Well-posedness of Lovelock gravity
• Quasilinear reformulation of Lovelock gravity
• Hairy Lovelock black holes and Stueckelberg mechanism for Weyl symmetry
• Black Holes and Wormholes in Higher-Curvature Corrected Theories of Gravity