Hyperbolicity and Causality of Einstein-Gauss-Bonnet Gravity in Warped Product Spacetimes
arXiv:2101.02461 · doi:10.1103/PhysRevD.103.064054
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.
arXiv commentRevtex, 32 pages, 5 figures; two references added, typos corrected
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- 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 Gravity with Dynamical Shifts
- Consistency between Bulk and Boundary Causalities in Asymptotically Anti-de Sitter Spacetimes