Stability of spherically symmetric solutions in modified theories of gravity

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.

ReVTex; 20 pages, 3 figures. v2: references added, submitted to PRD; v3: expanded discussion of TeVeS; v4: minor typos corrected (version to appear in PRD)

References in corpus (7)

• The Large Scale Structure of f(R) Gravity
• Solar System constraints to general f(R) gravity
• Solar System tests DO rule out 1/R gravity
• Can Cosmic Structure form without Dark Matter?
• The modified Newtonian dynamics-MOND-and its implications for new physics
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

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