Non-axisymmetric (2+1) black holes with Dym boundary conditions

TL;DR

This paper explores a new class of stationary, non-axisymmetric black hole solutions in AdS$_3$ gravity, characterized by Dym boundary conditions, combining holonomy analysis with solutions of the stationary Dym equation.

Contribution

It introduces the spectrum of non-axisymmetric black holes under Dym boundary conditions using a novel combination of holonomy and Dym equation solutions.

Findings

Characterization of black hole solutions with two real parameters and two integers

Identification of stationary, non-axisymmetric black holes in AdS$_3$

Integration of Chern-Simons holonomy conditions with Dym equation solutions

Abstract

We present the spectrum of stationary black hole solutions associated with the first non-trivial member of the Dym family of boundary conditions. The analysis combines the holonomy conditions provided by the Chern-Simons formulation of AdS$_3$ gravity with the periodic solutions of the stationary Dym equation. The resulting spacetimes are characterized by two positive real parameters, two positive integers, and a relative phase, generically describing stationary, non-axisymmetric black holes.