Equivalence of Nondifferentiable Metrics

TL;DR

This paper introduces new differential invariants for nondifferentiable metrics in general relativity, aiding in understanding causality issues inside black holes and constraining gravitational collapse scenarios.

Contribution

It develops a novel method using Cartan's equivalence adapted to Courant algebroids to analyze nondifferentiable metrics and their invariants.

Findings

New invariants characterize nondifferentiability loci

Resolved causality issues inside black holes with closed timelike geodesics

Established limits on gravitational collapse evolution

Abstract

We study nondifferentiable metrics occuring in general relativity via the method of equivalence of Cartan adapted to the Courant algebroids. We derive new local differential invariants naturally associated with the loci of nondifferentiability and rank deficiency of the metric. As an application, we utilize the newfangled invariants to resolve the problem of causality in the interior of the black holes that contain closed timelike geodesics. Also, a no-go type theorem limits the evolution scenarios for gravitational collapse.