# (Non-)uniqueness of Einstein-Palatini Gravity

## TL;DR

This paper investigates the general solutions of Einstein-Palatini gravity, demonstrating that all solutions are essentially Levi-Civita connections with an undetermined 1-form, leading to equivalent physical descriptions.

## Contribution

It shows that the most general connection in Einstein-Palatini formalism reduces to Levi-Civita plus an undetermined 1-form, establishing their physical equivalence.

## Key findings

- Connections are Levi-Civita up to a 1-form
- Solutions are physically equivalent to Levi-Civita
- Matter Lagrangian independence confirmed

## Abstract

We analyse the most general connection allowed by Einstein-Hilbert theory in Palatini formalism. We also consider a matter lagrangian independent of the affine connection. We show that any solution of the equation of the connection is essentially Levi-Civita up to a term that contains an undetermined 1-form. Finally, it is proved that these connections and Levi-Civita describe a completely equivalent physics.