Non-Riemannian Gravitational Interactions

TL;DR

This paper reviews recent advances in non-Riemannian gravity theories, focusing on fluid motion with torsion and metric gradients, and shows that matter-free cases lead to Einstein-Proca systems with standard connections.

Contribution

It provides a unified approach to non-Riemannian gravitational interactions and derives Einstein-Proca equations from broad action principles without matter.

Findings

Fluid motion affected by torsion and metric gradients analyzed.

Matter-free solutions reduce to Einstein-Proca systems.

Variational equations connect non-Riemannian fields to standard gravity.

Abstract

Recent developments in theories of non-Riemannian gravitational interactions are outlined. The question of the motion of a fluid in the presence of torsion and metric gradient fields is approached in terms of the divergence of the Einstein tensor associated with a general connection. In the absence of matter the variational equations associated with a broad class of actions involving non-Riemannian fields give rise to an Einstein-Proca system associated with the standard Levi-Civita connection.