Conformal Positive Mass Theorems for Manifolds with Charge

TL;DR

This paper establishes conformal positive mass theorems for charged asymptotically flat manifolds, linking scalar curvature, electric fields, and total charge, with applications to boundary conditions and scalar charge scenarios.

Contribution

It introduces new conformal positive mass theorems for charged manifolds, extending classical results to include electric charge and boundary conditions.

Findings

Mass is bounded below by electric charge under certain conformal conditions

Conformal relations relate scalar curvature and electric fields in mass inequalities

Results apply to manifolds with boundary and scalar charge scenarios

Abstract

In this paper, we prove conformal positive mass theorems for asymptotically flat manifolds with charge. We apply conformal relations to show that if the conformal sum of scalar curvature is not less than the norm square of electric field and electric density, the sum of the mass will not less than the modulus of total electric charge. We also study the situation with inner boundary condition and manifolds with scalar charge.