Probing Geometric Proca in Metric-Palatini Gravity with Black Hole Shadow and Photon Motion

Understand

Extended metric-Palatini gravity, quadratic in the antisymmetric part of the affine curvature, 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 affine connection, qualifies to be a distinctive signature of the affine curvature.
• In the present work, we explore how shadow and photon motion near black holes can be used to probe the geometric Proca field.
• To this end, we derive static spherically symmetric field equations of this Einstein-geometric Proca theory, and show that it admits black hole solutions in asymptotically AdS background.