Bootstrapping gravity solutions

TL;DR

This paper develops an algorithm to find all stationary axi-symmetric solutions in 3D Einstein gravity with scalar fields, explores their thermodynamics, and presents new solutions including flat hairy black holes and asymptotically AdS spacetimes.

Contribution

It introduces a systematic method to classify solutions and derives universal thermodynamic formulas, expanding the landscape of known gravity solutions with scalar fields.

Findings

Constructed an algorithm for solutions classification.

Derived universal entropy formulas.

Presented new flat hairy black holes and novel AdS solutions.

Abstract

We construct an algorithm to determine all stationary axi-symmetric solutions of 3-dimensional Einstein gravity with a minimally coupled self-interacting scalar field. We holographically renormalize the theory and evaluate then the on-shell action as well as the stress tensor and scalar one-point functions. We study thermodynamics, derive two universal formulas for the entropy and prove that global AdS provides a lower bound for the mass of certain solitons. Several examples are given in detail, including the first instance of locally asymptotically flat hairy black holes and novel asymptotically AdS solutions with non-Brown-Henneaux behavior.