# Extra equation of gravity induced by spontaneous local Lorentz symmetry breakdown

## TL;DR

This paper proposes a model where spontaneous Lorentz symmetry breaking leads to emergent gravity, reproducing general relativity up to third order and coupling correctly to matter, suggesting a novel approach to gravity from gauge fields.

## Contribution

It introduces a four-dimensional model with spontaneous Lorentz violation that generates gravity and interactions via gauge fields, aligning with Einstein's theory up to third order.

## Key findings

- Emergent gravity is equivalent to general relativity up to third order.
- Correct coupling to matter, including fermions, is achieved.
- Further work needed to compare black hole properties with Einstein's theory.

## Abstract

A model of spontaneous Lorentz violation in four dimension is given, which seems to provide a Lorentz invariant effective theory. An SU(2) Yang-Mills gauge field and an auxiliary U(1) vector field generate gravity and other interactions when they have vacuum expectation values. The emergent gravity is equivalent to conventional general relativity up to the third order terms in the Lagrangian. The coupling to matter, including spin-1/2 fermions, is also given correctly to this level. It remains to be seen whether this formalism reproduces the properties of black holes and other consequences obtained from Einstein's theory.