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. We perform a detailed study of the optical properties and shadow of this black hole and contrast them with the observational data by considering black hole environments with and without plasma. As a useful astrophysical application, we discuss constraints on the Proca field parameters using the observed angular size of the shadow of supermassive black holes M87$$^*$$
∗
and Sgr A$$^*$$
∗
in both vacuum and plasma cases. Overall, we find that the geometric Proca can be probed via the black hole observations.
The emergent universe scenario is a proposal for resolving the Big Bang singularity problem in the standard Friedmann–Lemaitre–Robertson–Walker cosmology. In the context of this scenario, the Universe originates from a nonsingular static state. In the present work, considering the realization of the emergent universe scenario, we address the possibility of having a nonsingular Kantowski–Sachs type static state. Considering four and five dimensional models (with and without brane), it is shown that both the existence and stability of a nonsingular state depend on the dimensions of the spacetime and the nature of the fluid supporting the geometry.
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