Uniqueness of electric-magnetic spacetimes with massive particle

TL;DR

This paper proves the uniqueness of static, asymptotically flat Einstein-Maxwell spacetimes with electric and magnetic charges containing a non-extremal massive particle sphere, showing they are isometric to Reissner-Nordström spacetime.

Contribution

It establishes a uniqueness theorem for spacetimes with massive particle spheres, extending previous photon sphere classifications to include entire sets of spacetime foliations.

Findings

Spacetimes with massive particle spheres are uniquely Reissner-Nordström.

The set of spacetime foliations corresponds to various particle energies.

The proof utilizes conformal positive energy and mass theorems.

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-Nordstr\"om 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.