Building multi-BTZ black holes through Riemann-Hilbert problem

A bstract We construct a recently found class of non-BPS black hole solutions with asymptotically AdS 3 × S 3 × 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 × S 1 × T 4 to AdS 3 × S 3 × 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.