Riemann-Cartan gravity with dynamical signature

TL;DR

This paper develops a Riemann-Cartan gravity model where the metric signature varies dynamically, favoring Minkowski space and exploring implications for black hole interiors with Euclidean signatures.

Contribution

It introduces a gravity formalism with dynamical metric signature, including new action terms, and demonstrates the Minkowski signature's dynamical preference.

Findings

Minkowski signature is dynamically favored over other signatures.

Configurations with Euclidean signature inside black holes are considered.

The model includes new terms depending on vierbein, spin connection, and internal metric.

Abstract

Model of Riemann-Cartan gravity with varying signature of metric is considered. The basic dynamical variables of the formalism are vierbein, spin connection, and an internal metric in the tangent space. The corresponding action contains new terms, which depend on these fields. In general case the signature of the metric is determined dynamically. The Minkowski signature is preferred dynamically because the configurations with the other signatures are dynamically suppressed. We also discuss briefly the motion of particles in the background of the modified black hole configuration, in which inside the horizon the signature is that of Euclidean space - time.