Rigidity in the Positive Mass Theorem with Charge

TL;DR

This paper proves a rigidity statement in the positive mass theorem with charge by coupling the Dirac equation with the generalized Jang equation, avoiding the maximal slicing condition.

Contribution

It introduces a novel coupling approach that simplifies the proof of the rigidity statement without maximal slicing assumptions.

Findings

Rigidity in the positive mass theorem with charge is established under new conditions.

Coupling the Dirac and generalized Jang equations provides a new proof technique.

The approach avoids the maximal slicing condition, broadening applicability.

Abstract

In this paper we show how a natural coupling of the Dirac equation with the generalized Jang equation, leads to a proof of the rigidity statement in the positive mass theorem with charge, without the maximal slicing condition, provided a solution to the coupled system exists.