Charged Hawking Mass on CMC Collars with Charged Matter

Abstract

We study strictly stable minimal horizons in three-dimensional time-symmetric charged initial data sets with cosmological constant, allowing charged matter. Along the constant-mean-curvature foliation issuing from the horizon through leaves with positive Jacobi operator, we prove exact first-variation identities for the charged Hawking mass. When the charge density has one sign compatible with the horizon charge, Hawking masses are nondecreasing, and equality between the two boundary values of the fixed-charge mass forces the entire collar to be isometric to an annulus in a source-free constant-curvature Reissner--Nordström--(anti-)de Sitter model. From this we recover the local rigidity results under a local maximality condition. At the minimal endpoint the defect entering these identities computes the fixed-charge Hawking-mass Hessian along the normalized lapse, and its vanishing characterizes the model horizon data.