The gravitational field of a star in quadratic gravity

TL;DR

This paper investigates static equilibrium solutions for self-gravitating fluids in quadratic gravity theories, revealing that Weyl tensor quadratic terms significantly affect the properties of compact objects and proposing a way to detect deviations from General Relativity.

Contribution

It provides a detailed analysis of how quadratic curvature terms influence the structure of compact objects, highlighting the dominant role of Weyl tensor corrections over Ricci scalar terms.

Findings

Weyl tensor quadratic terms strongly affect the radius and maximum mass of compact objects.

The inclusion of quadratic terms can alter the gravitational mass and Yukawa correction strength.

Ambiguity in mass definition in quadratic gravity can be used to detect deviations from GR.

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.