The gravitational field of a star in quadratic gravity

Abstract

The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity. We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity including terms quadratic in the Weyl tensor $C_{\mu \nu \rho \sigma }$ and in the Ricci scalar $R$, as suggested by one-loop corrections to classical gravity. By the means of a shooting method procedure we link the total gravitational mass and the strength of the Yukawa corrections associated with the quadratic terms with the fluid properties at the center. It is shown that the inclusion of the $C_{\mu \nu \rho \sigma }{C}^{\mu \nu \rho \sigma }$ coupling in the lagrangian has a much stronger impact than the $R^2$ correction in the determination of the radius and of the maximum mass of a compact object. We also suggest that the ambiguity in the definition of mass in quadratic gravity theories can conveniently be exploited to detect deviations from standard General Relativity.

18 pages, 7 figures, 1 table

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• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Black Holes in Higher-Derivative Gravity
• Analytical representations of unified equations of state of neutron-star matter
• Structure of neutron stars in R-squared gravity
• Static Solutions for 4th order gravity
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Cited by in corpus (2)

• Constraints on charged Symmergent black hole from shadow and lensing
• Regular black holes from higher-derivative effective delta sources