Uniqueness of the static spacetimes with a photon sphere in Einstein-scalar field theory

TL;DR

This paper proves a uniqueness theorem for static, asymptotically flat Einstein-scalar field solutions with a photon sphere, showing they are uniquely determined by mass and scalar charge and are isometric to a specific known solution.

Contribution

It establishes a new uniqueness result for Einstein-scalar field solutions with photon spheres, extending previous classifications in gravitational theories.

Findings

Solutions are uniquely specified by mass and scalar charge.

Solutions are isometric to Janis-Newman-Winicour solutions under certain conditions.

The scalar charge must satisfy the inequality q^2/M^2 < 3.

Abstract

In the present paper we prove a uniqueness theorem for the static and asymptotically flat solutions to the Einstein-scalar field equations which possess a photon sphere. We show that such solutions are uniquely specified by their mass $M$ and scalar charge $q$ and that they are isometric to the Janis-Newman-Winicour solution with the same mass and scalar charge subject to the inequality $\frac{q^2}{M^2}<3$.