Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity

Abstract

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot determine the functional form of $f(R)$. However, we also show that matching the outside Schwarzschild-de Sitter-metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.

5 pages

References in corpus (6)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The Large Scale Structure of f(R) Gravity
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Solar System constraints to general f(R) gravity
• Limit to General Relativity in f(R) theories of gravity
• Solar System tests DO rule out 1/R gravity

Cited by in corpus (48)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Wormhole geometries in f(R) modified theories of gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Good and bad tetrads in f(T) gravity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Relativistic stars in f(R) gravity, and absence thereof
• Collapsing spherical stars in f(R) gravity
• Thin accretion disks in f(R) modified gravity models
• Do f(R) theories matter?
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Dark energy, inflation and dark matter from modified F(R) gravity
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• Tolman-Oppenheimer-Volkoff equations in presence of the Chaplygin gas: stars and wormhole-like solutions
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Non-Vacuum Bianchi Types I and V in f(R) Gravity
• $f(R)$ gravity constrained by PPN parameters and stochastic background of gravitational waves
• Anisotropic Fluid and Bianchi Type III Model in f(R) Gravity
• Black hole entropy in modified gravity models
• Conserved Quantities in $f(R)$ Gravity via Noether Symmetry
• Stellar configurations in f(R) theories of gravity
• Thermodynamic topology of black Holes in f(R) gravity
• Non-vacuum Solutions of Bianchi Type VI_0 Universe in f(R) Gravity
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• $f(\mathsf{R})$ Gravity Wormholes sourced by a Phantom Scalar Field
• Black holes of $(2+1)$-dimensional $f(R)$ gravity coupled to a scalar field
• Quasinormal modes and their anomalous behavior for black holes in $f(R)$ gravity
• Curvature Scalarization of Black Holes in f(R) Gravity
• Topological Static Spherically Symmetric vacuum Solutions in $\mathcal{F}(R,G)$ Gravity
• Inflation with F(T) Teleparallel Gravity
• Rotating black hole in $f(R)$ theory
• $(2+1)$-Dimensional Black Holes in $f(R,\varphi )$ Gravity
• Specific neutral and charged black holes in $f(R)$ gravitational theory
• Uniqueness of non-trivial spherically symmetric black hole solution in special classes of F(R) gravitational theory
• Quantum singularities in a model of f(R) Gravity
• Exploring Plane Symmetric Solutions in $f(R)$ Gravity
• Black Holes with Electric and Magnetic Charges in $F(R)$ Gravity
• Noncompactified Kaluza--Klein Gravity
• New black hole solutions in three-dimensional $f(R)$ gravity
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity
• Constraining Parameters for the Accelerating Universe in $f(R,{\mathcal{L}}_m)$ Gravity
• Investigation of Bouncing Universe and Phantom Crossing in Modified Gravity Coupled with Weyl Tensor and its Reconstruction
• Is scalar-tensor gravity consistent with polytropic stellar models?
• Testing gravity with the latent heat of neutron star matter
• Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in $f(R)$ gravity
• Analytical calculation of Kerr and Kerr-Ads black holes in $f(R)$ theory