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 selfgravitating 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 oneloop 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.00558
 Bibcode:
 2021arXiv210600558B
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 18 pages, 7 figures, 1 table