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arXiv · 2004.04878

Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity

G. Rodrigues-da-Silva·L. G. Medeiros
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Abstract

Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the second-order corrections of general relativity, namely, $R^{2}$, $R^{3}$ and $R\square R$. Then, we explore spherically symmetric and static solutions in the weak-field regime and black holes context. All solutions in the weak-field regime due to a point mass are deduced, and by making a stability analysis of these solutions, we restrict them to Yukawa-type solutions. In regard to black hole solutions, we use the Lichnerovicz method to investigate the possibility of existence of non-Schwarzschild black holes. The results obtained show that non-Schwarzschild solutions might exist. However, for reasonable values of the parameters of the theory, its horizon radii are extremely small making macroscopic black holes different from Schwarzschild unfeasible.

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BibTeXRIS

G. Rodrigues-da-Silva, L. G. Medeiros. 2020-04-10. Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity. https://doi.org/10.1103/physrevd.101.124061

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