Black Hole Solutions In Extended Metric-Palatini Gravity

Extended metric-Palatini gravity, quadratic in the antisymmetric part of the affinecurvature, is known to lead to the general relativity plus a geometric Proca field.The geometric Proca, equivalent of the non-metricity vector in the torsion-free affineconnection, qualifies to be a distinctive signature of the affine curvature. In thisthesis, we explore how photon and particle motion near black holes can be used toprobe the geometric Proca field. To this end, we derive static spherically symmetricfield equations of this Einstein-geometric Proca theory, and show that it admitsblack hole solutions in asymptotically AdS background. We perform a detailedstudy of the optical properties and shadow of this black hole and contrast themwith the observational data by considering black hole environments with and withoutplasma. As a useful astrophysical application, we discuss constraints on the Procafield parameters using the observed angular size of the shadow of supermassiveblack holes M87∗ and Sgr A∗ in both vacuum and plasma cases. We then performa detailed analysis using the observational quasiperiodic oscillations (QPOs) data.We use the latest data from stellar-mass black hole GRO J1655-40, intermediatemassblack hole in M82-X1, and the super-massive black hole in SgA* (our MilkyWay) and perform a Monte-Carlo-Markov-Chain (MCMC) analysis to determine orbound the model parameters. Our results shed light on the allowed ranges of theProca mass and other parameters. The results imply that our solutions can coverall three astrophysical black holes. Overall, we find that the geometric Proca can beprobed via the black hole observations. Our analysis can also be extended to moregeneral metric-affine gravity theories.