Building multi-BTZ black holes through Riemann-Hilbert problem

TL;DR

This paper constructs multi-BTZ black hole solutions in type IIB supergravity by solving a Riemann-Hilbert problem within the Breitenlohner-Maison framework, introducing a novel subtraction procedure for multiple black holes.

Contribution

It presents the first application of a subtraction procedure to multiple black holes, enabling the construction of multi-BTZ solutions from multi-neutral black strings.

Findings

Derived multi-BTZ black hole solutions in AdS_3×S^3×T^4.

Extended the Riemann-Hilbert problem approach to multiple horizons.

Introduced a new subtraction method for multiple black hole configurations.

Abstract

We construct a recently found class of non-BPS black hole solutions with asymptotically $AdS_3\times S^3\times T^4$ in type IIB supergravity, consisting of multiple BTZ black holes localized on an $S^3$, within the group theoretical framework of Breitenlohner and Maison (BM). Starting with the multi-neutral black string solution as a seed, we solve the associated Riemann-Hilbert problem for the BM linear system. First, we determine the monodromy matrix corresponding to this seed solution by generalizing the early work of Katsimpouri et al. on the four-charged black hole of STU supergravity, where some assumptions must be relaxed for the solutions with multiple horizons. By applying the Harrison transformation, a charge-generating transformation in the $SO(4,4)$ group, to the monodromy matrix, we obtain the multi-charged black string solution. Furthermore, through a ``subtraction'' procedure -- an $SO(4,4)$ transformation that changes the asymptotic structure from $R^{1,4}\times S^1\times T^4$ to $AdS_3\times S^3\times T^4$ spacetime -- we derive the multi-BTZ black hole solution. This is the first example in which the subtraction procedure is applied to multiple black holes, and it may also have potential applications to other cases.