Uniqueness of electric-magnetic spacetimes with massive particle

TL;DR

The paper proves that any static, asymptotically flat Einstein–Maxwell spacetime with both electric and magnetic charges, containing a non-extremal massive particle sphere as an inner boundary, is isometric to the corresponding Reissner–Nordström spacetime. It extends the photon-sphere paradigm to a foliation by massive particle spheres, showing the inner boundary has constant mean and scalar curvatures due to a functional relation between the lapse and the gauge potentials. The authors establish this rigidity via two complementary routes: (i) a conformal positive energy theorem that yields a flat, totally umbilical, spherically embedded boundary, and (ii) a positive mass theorem approach with alternative conformal transformations, both leading to the RN isometry. The magnetic charge modifies the potentials and some quantitative aspects but does not alter the essential uniqueness result, highlighting a robust RN-level rigidity in the presence of stationary electric–magnetic fields and massive particle boundaries. These results extend classical black hole uniqueness theorems and sharpen the understanding of how charged, magnetized spacetimes accommodate families of massive-particle foliations.

Abstract

Uniqueness of the four-dimensional static, asymptotically flat, Einstein-Maxwell spacetime with both electric and magnetic charges, containing non-extremal massive particle sphere, being an inner boundary in it, has been proved. It is isometric to Reissner-Nordström spacetime with electric/magnetic charges. In contrast to the previous results concerning the classification of photon spheres, it describes the existence of the entire set of spacetme foliations, a set of massive particle sphere addressed to the various energies of the particles. The conformal positive energy, positive mass theorem and adequate conformal transformations constitute the mail tools in the proof.