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.

arXiv comment5 pages

References in corpus (37)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The Cosmological Constant and Dark Energy
• Cosmological parameters from SDSS and WMAP
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• 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
• Curvature Quintessence
• Can modified gravity explain accelerated cosmic expansion?
• 1/R gravity and Scalar-Tensor Gravity
• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• The Cosmology of Generalized Modified Gravity Models
• The Large Scale Structure of f(R) Gravity
• One-loop f(R) gravity in de Sitter universe
• On Physical Equivalence between Nonlinear Gravity Theories
• Where new gravitational physics comes from: M-theory?
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• The Power of General Relativity
• Solar System constraints to general f(R) gravity
• The conformal frame freedom in theories of gravitation
• The gravity lagrangian according to solar system experiments
• Dynamics of Linear Perturbations in f(R) Gravity
• Limit to General Relativity in f(R) theories of gravity
• Evidence for a non-zero Lambda and a low matter density from a combined analysis of the 2dF Galaxy Redshift Survey and Cosmic Microwave Background Anisotropies
• Accelerated Cosmological Models in Ricci squared Gravity
• Solar System tests DO rule out 1/R gravity
• The stability of modified gravity models
• Higher order gravity theories and scalar tensor theories
• Solar System experiments do not yet veto modified gravity models
• The Force of Gravity from a Lagrangian containing Inverse Powers of the Ricci Scalar
• Cosmological Evolution in 1/R-Gravity Theory
• The nearly Newtonian regime in Non-Linear Theories of Gravity
• Post-Newtonian Parameters from Alternative Theories of Gravity
• Cosmological expansion and the uniqueness of gravitational action

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