The Penrose inequality and positive mass theorem with charge for manifolds with asymptotically cylindrical ends

TL;DR

This paper proves the charged Penrose inequality and positive mass theorem with charge for manifolds with asymptotically cylindrical ends, using doubling arguments and existing inequalities, extending results to new geometric settings.

Contribution

It introduces a novel approach combining doubling techniques and existing inequalities to establish fundamental geometric inequalities for manifolds with cylindrical ends.

Findings

Charged Penrose inequality established for asymptotically cylindrical manifolds.

Positive mass theorem with charge proven for these manifolds.

Rigidity statement included for equality cases.

Abstract

We establish the charged Penrose inequality for time symmetric initial data sets having an outermost minimal surface boundary and finitely many asymptotically cylindrical ends, with an appropriate rigidity statement. This is accomplished by a doubling argument based on the work of Weinstein and Yamada, and a subsequent application of the ordinary charged Penrose inequality as established by Khuri, Weinstein, and Yamada. Furthermore, the techniques used in the aforementioned proof allow for the proof of the positive mass theorem with charge for such manifolds.