The curious case of the Buchdahl-Land-Sultana-Wyman-Iba\~nez-Sanz spacetime

TL;DR

This paper revisits a specific scalar field solution of Einstein's equations, exploring its geometric properties and limitations in modeling relativistic stars, especially considering the influence of a hidden cosmological constant.

Contribution

It clarifies the geometric structure of the Wyman and Sultana solutions and highlights their limitations for stellar modeling due to a hidden cosmological constant.

Findings

The spacetime has a finite 3-space.

The geometry prevents modeling relativistic stars.

A hidden cosmological constant influences the solutions.

Abstract

We revisit Wyman's "other" scalar field solution of the Einstein equations and its Sultana generalization to positive cosmological constant, which has a finite 3-space and corresponds to a special case of a stiff fluid solution proposed by Buchdahl and Land and, later, by Iba\~nez and Sanz to model relativistic stars. However, there is a hidden cosmological constant and the peculiar geometry prevents the use of this spacetime to model relativistic stars.