Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes with arbitrary coupling constant

TL;DR

This paper proves the uniqueness of photon spheres in Einstein-Maxwell-dilaton black holes with arbitrary coupling, using conformal positive energy theorem to establish conditions for the geometry of these spheres.

Contribution

It demonstrates the uniqueness of static photon spheres in Einstein-Maxwell-dilaton black holes for any coupling constant, extending previous results to more general theories.

Findings

Photon sphere uniqueness is established for Einstein-Maxwell-dilaton black holes.

The conformal positive energy theorem is used to characterize the photon sphere geometry.

A non-extremality condition leads to a cylindrical topology over a sphere.

Abstract

The uniqueness of static asymptotically flat photon sphere for static black hole solution in Einstein-Maxwell-dilaton theory with arbitrary coupling constant was proposed. Using the conformal positive energy theorem we show that the dilaton sphere subject to the non-extremality condition authorizes a cylinder over a topological sphere.