We numerically construct asymptotically global ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ black holes in type IIB supergravity, with ${\mathbb{R}}_t\times \mathrm{SO}(2)\times \mathrm{SO}(3)\times \mathrm{U}(1{)}^4$ symmetry, localized on the ${\mathrm{S}}^3$ and translationally invariant along the torus. These solutions, with horizons whose spatial cross sections have ${\mathrm{S}}^4\times {\mathrm{T}}^4$ topology, dominate the microcanonical ensemble at low energies. At higher energies, a first-order phase transition occurs to $\mathrm{BTZ}\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ black holes—possessing ${\mathbb{R}}_t\times \mathrm{SO}(2)\times \mathrm{SO}(4)\times \mathrm{U}(1{)}^4$ symmetry and ${\mathrm{S}}^1\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ horizon topology. By the AdS/CFT correspondence, this transition reflects the spontaneous breaking of the SO(4) $R$ symmetry of the $D1\text{−}D5$ ${\mathrm{CFT}}_2$ to SO(3). We also compute the expectation value of the scalar operator with lowest conformal dimension in the low-energy phase. Our SO(3)-localized black holes—together with the $\mathrm{U}(1{)}^2$-localized solutions of Bena et al. [J. High Energy Phys. 10 (2025) 165.]—point to a rich landscape of novel black holes that may approach the ${\mathrm{CFT}}_2$ “sparseness bootstrap condition,” and shed light on how macroscopic entanglement in thermal phases encodes microscopic structure via internal directions.

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• Classical black holes
• Gauge-gravity dualities
• Quantum aspects of black holes
• Supergravity
• Numerical relativity