The gravitational field of a star in quadratic gravity

Understand

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.