Revisiting the static spherically symmetric solutions of gravity with a conformally coupled scalar field

TL;DR

This paper explores static spherically symmetric solutions in Einstein's gravity with a conformally coupled scalar field, revealing duality symmetries and rederiving a family of solutions with novel insights.

Contribution

It introduces a tensor-based reformulation of the field equations, identifies a duality symmetry in solutions, and rederives the full solution family using a new ansatz.

Findings

Identification of a duality symmetry in solutions.

Re-derivation of the three-parameter solution family.

Connection of known solutions like BBMB black hole and wormhole to the duality subfamily.

Abstract

We revisit the static spherically symmetric solutions of Einstein's General Relativity with a conformally coupled scalar field in arbitrary dimensions. Using a four rank tensor introduced earlier we recast the field equations in a manifestly symmetric form to elucidate a somewhat less-known feature of dual mapping between solutions. We also show that there is a two-parameter subfamily of solutions which enjoy a duality symmetry and in four dimensions both the BBMB black hole and the Barcelo-Visser wormhole belong to this subfamily. Along the way, we rederive the full three-parameter family of solutions by direct integration of the field equations and a natural choice of ansatz which arguably has several advantages over other previously known methods.