Building multi-BTZ black holes through Riemann-Hilbert problem
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arXiv
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| Format: | Preprint |
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2025
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| author | Sakamoto, Jun-ichi Tomizawa, Shinya |
| author_facet | Sakamoto, Jun-ichi Tomizawa, Shinya |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Building multi-BTZ black holes through Riemann-Hilbert problem Sakamoto, Jun-ichi Tomizawa, Shinya High Energy Physics - Theory General Relativity and Quantum Cosmology 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. |
| title | Building multi-BTZ black holes through Riemann-Hilbert problem |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.19310 |