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# Vacuum solutions around spherically symmetric and static objects in Starobinsky model

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### Abstract

The vacuum solutions around a spherically symmetric and static object are studied in Starobinsky model with perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star. The modified vacuum solution leads to deviations from general relativity that could be measured in light bending observations.

### Most cited references6

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### Can higher curvature corrections cure the singularity problem in f(R) gravity?

(2008)
Although $$f(R)$$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $$f(R)$$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $$\mu \lesssim 10^{-19}$$ GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $$f(R)$$ models without very careful and unnatural fine-tuning.
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### Author and article information

###### Journal
28 July 2017
1708.00345