Stability of spherically symmetric solutions in modified theories of gravity

TL;DR

This paper investigates the stability of spherically symmetric solutions in three alternative gravity theories, revealing instabilities in matter-filled f(R) gravity and issues in Einstein-aether and TeVeS theories.

Contribution

It applies a generalized variational principle to analyze the stability of solutions in f(R), Einstein-aether, and TeVeS theories, highlighting their stability conditions and instabilities.

Findings

f(R) gravity is highly unstable with matter

Einstein-aether stability conditions match linearized flat spacetime

TeVeS has indefinite kinetic terms leading to instability

Abstract

In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our "generalized variational principle", described in a previous work, to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s f(R) gravity, Jacobson & Mattingly's "Einstein-aether theory", and Bekenstein's TeVeS. We find that in the presence of matter, f(R) gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-aether backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the "kinetic terms" of vacuum TeVeS are indefinite in a curved background, leading to an instability.