# A 3+1 Decomposition of the Minimal Standard-Model Extension Gravitational Sector

## TL;DR

This paper develops a 3+1 decomposition of the minimal Standard-Model Extension gravity Lagrangian, facilitating comparisons with other gravity models and aiding in canonical quantum gravity and numerical relativity.

## Contribution

It introduces a novel 3+1 (ADM) decomposition of the SME gravity Lagrangian aligned with a timelike vector field, enabling better integration with existing gravity frameworks.

## Key findings

- Decomposition aligns SME gravity with ADM formalism
- Facilitates comparison with other gravity theories
- Supports applications in quantum gravity and numerical relativity

## Abstract

The 3+1 (ADM) formulation of General Relativity is used in, for example, canonical quantum gravity and numerical relativity. Here we present a 3+1 decomposition of the minimal Standard-Model Extension gravity Lagrangian. By choosing the leaves of foliation to lie along a timelike vector field we write the theory in a form which will allow for comparison and matching to other gravity models.