Static Spherically Symmetric Solutions in F(R) Gravity

Abstract

A Lagrangian derivation of the Equation of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in $F(R)$-gravity. All known exact solutions are recovered. We also exibit a new non trivial solution with non constant Ricci scalar.

8 pages, published version, some references added, a minor modification

References in corpus (16)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Matter instability in modified gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Spherical symmetry in $f(R)$-gravity
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• On the Hawking radiation as tunneling for a class of dynamical black holes
• On the way from matter-dominated era to dark energy universe
• On the Stability of a class of Modified Gravitational Models
• New Energy Definition for Higher Curvature Gravities
• f(R) Gravity: From the Pioneer Anomaly to the Cosmic Acceleration
• Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity
• Black Hole entropy for two higher derivative theories of gravity

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