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

TL;DR

This paper investigates the hyperbolicity and causality of tensor perturbations in Einstein-Gauss-Bonnet gravity within warped product spacetimes, providing exact conditions for various solutions and extending analysis to dynamical spacetimes like Vaidya.

Contribution

It introduces a generalized master equation for tensor perturbations that applies without static conditions, enabling comprehensive hyperbolicity and causality analysis in Einstein-Gauss-Bonnet gravity.

Findings

Derived exact hyperbolic conditions for vacuum solutions.

Defined effective (acoustic) metric without static assumptions.

Extended analysis to dynamical spacetimes like Vaidya.

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.