Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles

TL;DR

This paper explores Einstein-scalar field solutions in AdS spacetime, analyzing black holes, solitons, and scalar clouds, with a focus on boundary conditions, asymptotics, and exact solutions for monopole and dipole cases.

Contribution

It provides new insights into boundary conditions and solutions for Einstein-scalar fields in AdS, including exact monopole and dipole solitons and their relation to scalar clouds.

Findings

Existence of monopole and dipole solitons as perturbations around AdS.

Numerical and exact solutions for scalar clouds and solitons.

Clarification of boundary conditions and asymptotics in AdS scalar field models.

Abstract

We consider an Einstein-scalar field model which is a consistent truncation of ${\cal N}=8$ $D=4$ gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic self-interaction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.