Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory

TL;DR

This paper classifies static, asymptotically flat solutions with a photon sphere in Einstein-multiple-scalar field theory, showing they are uniquely determined by their asymptotic data and explicitly constructing such solutions.

Contribution

It provides a uniqueness classification and explicit construction of solutions with photon spheres in Einstein-multiple-scalar field theory under certain geometric conditions.

Findings

Solutions are uniquely specified by mass, scalar charges, and asymptotic scalar values.

Explicit solutions with photon spheres are constructed for the specified class.

The classification applies when the target space has non-positive sectional curvature.

Abstract

In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional curvature we prove that the static and asymptotically flat solutions which posses a photon sphere are uniquely specified by their asymptotic data, i.e. by their mass, scalar charges and asymptotic values of the scalar fields. The unique solution with a photon sphere and prescribed asymptotic data is explicitly constructed.