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

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• 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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• "Detuned" f(R) gravity and dark energy
• A new approach in stability analysis: case study: tachyon cosmology with non-minimally coupled scalar field-matter
• Structure of Compact Stars in R-squared Palatini Gravity
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• Investigation of Bouncing Universe and Phantom Crossing in Modified Gravity Coupled with Weyl Tensor and its Reconstruction
• Role of $\sigma R^2+\gamma R_{\mu \nu }{T}^{\mu \nu }$ Model on Anisotropic Polytropes
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• Study of Anisotropic Polytropes in $f(\mathcal{R},\mathrm{T})$ Theory
• Testing gravity with the latent heat of neutron star matter
• A perturbative approach for the study of compatibility between nonminimally coupled gravity and Solar System experiments