Geometric Proca with Matter in Metric-Palatini Gravity

TL;DR

This paper explores an extended metric-Palatini gravity theory that reduces to Einstein gravity plus a massive vector field, which universally couples to matter, affecting black hole horizons and potentially impacting astrophysical and collider phenomena.

Contribution

It introduces a novel extension of metric-Palatini gravity with a geometric Proca field and analyzes its effects on black hole solutions and matter coupling.

Findings

The extended gravity reduces to Einstein gravity plus a massive vector field.

The geometric Proca field couples universally to fermions.

Dust presence hampers horizon formation in black hole solutions.

Abstract

In the present work, we study linear, torsion-free metric-Palatini gravity, extended by the quadratics of the antisymmetric part of the Ricci tensor and extended also by the presence of the affine connection in the matter sector. We show that this extended metric-Palatini gravity reduces dynamically to the general relativity plus a geometrical massive vector field corresponding to non-metricity of the connection. We also show that this geometric Proca field couples to fermions universally. We derive static, spherically symmetric field equations of this Einstein-geometric Proca theory. We study possibility of black hole solutions by taking into account the presence of a dust distribution that couples to the geometric Proca. Our analytical and numerical analyses show that the presence of this dust worsens the possibility of horizon formation. We briefly discuss possible roles of this universally-coupled geometric Proca in the astrophysical and collider processes.