Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions

TL;DR

This paper explores asymptotically locally flat black hole solutions in three-dimensional massive gravity, introducing non-spherical 'black flowers', analyzing their properties, and deriving thermodynamic laws within a relaxed asymptotic framework.

Contribution

It demonstrates the existence of non-spherical black hole solutions called black flowers and extends the asymptotic analysis to include radiating spacetimes in three-dimensional massive gravity.

Findings

Black flowers are non-spherical deformations of black holes.

Conserved charges form a BMS$_{3}$ algebra without central extensions.

First law of thermodynamics is derived for solutions with horizons.

Abstract

The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.