Stability of f(R) black holes

Abstract

We investigate the stability of $f(R)$ (Schwarzschild) black hole obtained from the $f(R)$ gravity. It is difficult to carry out the perturbation analysis around the black hole because the linearized Einstein equation is fourth order in $f(R)$ gravity. In order to resolve this difficulty, we transform $f(R)$ gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar becomes a scalaron, showing that all linearized equations are second order, which are the same equations for the massive Brans-Dicke theory. It turns out that the $f(R)$ black hole is stable against the external perturbations if the scalaron does not have a tachyonic mass.

arXiv comment16 pages, no figures, version to appear in Physical Review D

References in corpus (28)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• f(R) Theories Of Gravity
• f(R) theories
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Quasinormal modes of black holes: from astrophysics to string theory
• Can modified gravity explain accelerated cosmic expansion?
• One-loop f(R) gravity in de Sitter universe
• Post-Newtonian constraints on f(R) cosmologies in metric formalism
• Post-Newtonian constraints on f(R) cosmologies in Palatini formalism
• The basics of gravitational wave theory
• The pattern of growth in viable f(R) cosmologies
• The gravity lagrangian according to solar system experiments
• Limit to General Relativity in f(R) theories of gravity
• Black Holes in f(R) theories
• The stability of modified gravity models
• Static Spherically Symmetric Solutions in F(R) Gravity
• Covariant Perturbations of Schwarzschild Black Holes
• Existence of stable hairy black holes in su(2) Einstein-Yang-Mills theory with a negative cosmological constant
• Kerr Black Holes are Not Unique to General Relativity
• A bird's eye view of f(R)-gravity
• Perturbed Kerr Black Holes can probe deviations from General Relativity
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes
• Hamiltonian analysis of non-projectable modified F(R) Hořava-Lifshitz gravity
• Stability and Quasinormal Modes of Black holes in Tensor-Vector-Scalar theory: Scalar Field Perturbations
• Graviton and scalar propagations on AdS(4) space in f(R) gravities
• Generalized modified gravity models: the stability issue

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