Hyperbolicity and Causality of Einstein-Gauss-Bonnet Gravity in Warped Product Spacetimes

Abstract

In Einstein-Gauss-Bonnet gravity, for a group of warped product spacetimes, we get a generalized master equation for the perturbation of tensor type. We show that the "effective metric" or "acoustic metric" for the tensor perturbation equation can be defined even without a static condition. Since this master equation does not depend on the mode expansion, the hyperbolicity and causality of the tensor perturbation equation can be investigated for every mode of the perturbation. Based on the master equation, we study the hyperbolicity and causality for all relavent vacuum solutions of this theory. For each solution, we give the exact hyperbolic condition of the tensor perturbation equations. Our approach can also applied to dynamical spacetimes, and Vaidya spacetime have been investigated as an example.

Revtex, 32 pages, 5 figures; two references added, typos corrected

References in corpus (12)

• Viscosity Bound and Causality Violation
• Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Causality and Hyperbolicity of Lovelock Theories
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Catastrophic Instability of Small Lovelock Black Holes
• Causal Structures in Gauss-Bonnet gravity
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
• Non-Minimally Coupled Einstein Gauss Bonnet Inflation Phenomenology in View of GW170817
• Matter without matter: novel Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity
• Stability of Lovelock Black Holes under Tensor Perturbations
• Kaluza-Klein black hole with negatively curved extra dimensions in string generated gravity models

Cited by in corpus (6)

• On the "Einstein-Gauss-Bonnet Gravity in Four Dimension"
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• A Note on the Strong Hyperbolicity of $f(R)$ Gravity with Dynamical Shifts
• Consistency between Bulk and Boundary Causalities in Asymptotically Anti-de Sitter Spacetimes