On uniqueness of static spacetime with conformal scalar in higher dimensions

TL;DR

This paper proves the uniqueness of certain higher-dimensional static spacetimes with a conformal scalar field, even in the presence of a singular point where the effective Newton constant diverges.

Contribution

It establishes a uniqueness theorem for asymptotically flat, static spacetimes with conformal scalar fields in higher dimensions, including cases with singular points.

Findings

Uniqueness of static solutions outside a specific surface in higher dimensions.

Identification of conditions under which the spacetime is unique.

Analysis of singular points where the effective Newton constant diverges.

Abstract

We discuss the uniqueness of asymptotically flat and static spacetimes in the $n$-dimensional Einstein-conformal scalar system. This theory potentially has a singular point in the field equations where the effective Newton constant diverges. We will show that the static spacetime with the conformal scalar field outside a certain surface $S_p$ associated with the singular point is unique.