Stability of Schwarzschild-like solutions in f(R,G) gravity models

TL;DR

This paper analyzes the stability of Schwarzschild-like solutions in f(R,G) gravity models, revealing conditions under which ghost modes appear and classifying propagating modes for perturbations.

Contribution

It provides a detailed stability analysis of f(R,G) theories, identifying conditions to avoid ghosts and classifying perturbation modes and their speeds.

Findings

Even-type perturbations have ghosts unless the Hessian determinant is zero.

Theories can be viable if ghosts are sufficiently massive to decouple.

Classification of propagating modes and their speeds for different perturbation types.

Abstract

We study linear metric perturbations around a spherically symmetric static spacetime for general f(R,G) theories, where R is the Ricci scalar and G is the Gauss-Bonnet term. We find that unless the determinant of the Hessian of f(R,G) is zero, even-type perturbations have a ghost for any multi-pole mode. In order for these theories to be plausible alternatives to General Relativity, the theory should satisfy the condition that the ghost is massive enough to effectively decouple from the other fields. We study the requirement on the form of f(R,G) which satisfies this condition. We also classify the number of propagating modes both for the odd-type and the even-type perturbations and derive the propagation speeds for each mode.