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

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

2006-11-28

arxiv.org/abs/gr-qc/0611149v2

Class.Quant.Grav.24:2333-2342,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version, to appear in Classical and Quantum Gravity.

Scientific paper

10.1088/0264-9381/24/9/011

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.

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