Who's afraid of a negative lapse?

TL;DR

This paper revisits the ADM equations, presenting a covariantized version of the Anderson-York equations that are well-posed and analyze their causality and relation to maximal globally hyperbolic developments.

Contribution

It introduces a covariant framework for the Anderson-York equations, ensuring well-posedness and analyzing their causality properties in general relativity.

Findings

Rederived ADM equations with zero lapse issues addressed

Developed a covariantized Anderson-York system with freely prescribable shift and densitized lapse

Analyzed causality and connection to maximal globally hyperbolic developments

Abstract

We rederive the Arnowitt-Deser-Misner equations in a framework in which the zeros of the lapse are innocuous, whether with or without changes of sign. We further develop and analyse a covariantized version of the Anderson-York equations, which provide a well posed system of tensorial evolution equations with freely prescribable shift vector and densitised lapse. The causality properties of the resulting equations are explored. We show how to relate solutions of the Anderson-York equations to the maximal globally hyperbolic development of the initial data.