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.

arXiv commentReVTex; 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 (20)

• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Relativistic gravitation theory for the MOND paradigm
• Gravity with a dynamical preferred frame
• Can modified gravity explain accelerated cosmic expansion?
• 1/R gravity and Scalar-Tensor Gravity
• The Large Scale Structure of f(R) Gravity
• Einstein-Aether Waves
• Solar System constraints to general f(R) gravity
• Large Scale Structure in Bekenstein's theory of relativistic Modified Newtonian Dynamics
• Solar System tests DO rule out 1/R gravity
• Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect
• Black Holes in Einstein-Aether Theory
• Can Cosmic Structure form without Dark Matter?
• The modified Newtonian dynamics-MOND-and its implications for new physics
• Spherical Solutions in Einstein-Aether Theory: Static Aether and Stars
• Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Spherically symmetric, static spacetimes in a tensor-vector-scalar theory
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

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• What Do We Know About Lorentz Invariance?
• Non-linear evolution of f(R) cosmologies II: power spectrum
• General Relativity and Cosmology: Unsolved Questions and Future Directions
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• Stability of the Einstein static universe in f(R) gravity
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• Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817
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• Static Spherically Symmetric Einstein-aether models I: Perfect fluids with a linear equation of state and scalar fields with an exponential self-interacting potential
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• Black holes and neutron stars in the generalized tensor-vector-scalar theory
• Aether scalar tensor theory: Linear stability on Minkowski space
• Role of Structure Scalars on the evolution of Compact Objects in Palatini $f(R)$ Gravity
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• The Geometry Of Modified Newtonian Dynamics
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• Einstein-aether gravity: theory and observational constraints
• Spherically symmetric exact vacuum solutions in Einstein-aether theory
• Stability and Quasinormal Modes of Black holes in Tensor-Vector-Scalar theory: Scalar Field Perturbations
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• Consistency Condition of Spherically Symmetric Solutions in $f(R)$ Gravity
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• Post-Newtonian parameters in the tensor-vector-scalar theory
• Testing alternative theories of gravity with space-based gravitational wave detectors
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• Reconstruction of $f(R)$ lagrangian from a massive scalar field
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