Stellar configurations in f(R) theories of gravity

Abstract

We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-{\mu }^4/R$ model. We show how the stellar configuration in the $f(R)$ theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden -equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in $f(R)$ theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with Solar System constraints on the properties of gravity. Numerical work shows that stellar configurations, with a regular metric at the center, lead to ${\gamma }_{PPN}\simeq 1/2$ outside the star ie. the Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as the outside solution, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a $f(R)$ theory compatible with the Solar System experiments and possible new constraints arising from the radius-mass -relation of stellar objects is discussed.

8 pages, 7 figures; typos corrected, reference added

References in corpus (7)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• The Large Scale Structure of f(R) Gravity
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Solar System constraints to general f(R) gravity
• Solar System tests DO rule out 1/R gravity
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• Spherically symmetric spacetimes in f(R) gravity theories

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• Thin accretion disks in f(R) modified gravity models
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• "Detuned" f(R) gravity and dark energy
• On the stability of spherically symmetric spacetimes in metric f(R) gravity