Matter coupling to degenerate spacetimes in first order gravity

TL;DR

This paper investigates the equations of motion in first order gravity coupled with matter fields for degenerate spacetimes, revealing a distinct phase from standard gravity for non-invertible metrics.

Contribution

It systematically extends first order gravity with matter to degenerate metrics, detailing the equations for various matter fields and highlighting differences from second order theories.

Findings

Describes matter coupling in degenerate spacetimes.

Shows equivalence to second order gravity for invertible metrics.

Identifies a new phase in gravity for non-invertible metrics.

Abstract

We develop a systematic study of the equations of motion in the first order gravity with matter fields for degenerate metrics. Like the Hilbert-Palatini action functional for pure gravity, the action functionals for matter fields used are first order. These are defined for both invertible and non- invertible metrics. Description for invertible metrics is equivalent to second order gravity theory with matter. For degenerate metrics the theory describes a different phase. The analysis for tetrads with one zero eigen value in theory with scalar, Abelian vector gauge and fermion matter fields is presented in detail.