Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity

Abstract

We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to obtain the field equations in this gauge. The equilibrium hydrostatic equation is obtained and is used to study the Newtonian limit for $f(R)=R-\frac{a^2}{3R}$. The same procedure is carried out for the more generally case $f(R)=R-\frac{1}{n+2}\frac{a^{n+1}}{R^n}$ giving a good Newtonian limit.

Revised version, to appear in Classical and Quantum Gravity.

Cited by in corpus (19)

• 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
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Spherical symmetry in $f(R)$-gravity
• Relativistic stars in f(R) gravity, and absence thereof
• Do f(R) theories matter?
• The phase space view of f(R) gravity
• 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?
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Power-law cosmic expansion in f(R) gravity models
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Dynamics of f(R)-cosmologies containing Einstein static models
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Black hole entropy in modified gravity models
• Compactifying the state space for alternative theories of gravity