Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

TL;DR

This paper explores Einstein-scalar gravity solutions, revealing that while no-hair theorems prevent hairy black branes with AdS asymptotics, specific models admit non-AdS solutions with extremal limits being scalar solitons.

Contribution

The authors derive explicit exact solutions in Einstein-scalar gravity showing the existence of hairy black branes with non-AdS asymptotics and their extremal limits as scalar solitons.

Findings

Existence of hairy black branes with non-AdS domain wall asymptotics.

Scalar solitons as extremal limits of black branes.

Explicit exact solutions in an integrable Toda-like model.

Abstract

We investigate static, planar, solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for hairy black brane solutions with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall solution at $r=\infty$ and an AdS solution near $r=0$.