标题： 带电旋转毛发黑洞在AdS$_5 \times S^5$：揭示它们的秘密 显示英文标题

标题： Charged Rotating Hairy Black Holes in AdS$_5 \times S^5$: Unveiling their Secrets

摘要： 利用分析方法和数值方法的结合，我们构造了新的旋转带电“毛发”黑洞解，这些解属于$D=5$和${\cal N}=8$规范超引力理论，它们通过 AdS/CFT 对偶对应于$D=4$中有限化学势和角势的热态，${\cal N}=4$的对称性理论，从而补充并扩展了 [arXiv:1005.1287, arXiv:1806.01849, arXiv:1809.04084] 的结果。 这些解提升为IIB超引力中渐近AdS$_5 \times S^5$的解，其沿AdS$_5$（$J=J_1=J_2$）和$S^5$（$Q=Q_1=Q_2=Q_3$）的角动量相等。 当我们降低质量$E$而保持固定$Q$和$J$时，已知的Cvetič-Lü-Pope（CLP）黑洞对标量凝聚不稳定，此处构造的毛发黑洞作为与这种不稳定性相关的新型解出现。 在CLP黑洞和毛发黑洞共存的相空间区域，毛发黑洞主导微观正则系综，因此描述了 SYM 的一种新的热力学相。 毛发黑洞延伸至CLP极值面之外，直至由$E = 3 Q + 2 J / L$定义的BPS面。通过分析和数值技术的结合，我们论证了毛发黑洞的BPS极限是一种奇异、无视界的解，并且$not$是一种新的两参数族的BPS黑洞，扩展了已知的一参数 Gutowski-Reall（GR）黑洞解，这与[arXiv:1005.1287, arXiv:1806.01849]中的猜想相矛盾。 为了进一步支持我们的结论，我们对BPS方程进行了近地平线分析，并论证了它们不允许任何有地平线的规则解。 显示英文摘要

摘要： Using a mix of analytical and numerical methods, we construct new rotating, charged "hairy" black hole solutions of $D=5$, ${\cal N}=8$ gauged supergravity that are dual, via the AdS/CFT correspondence, to thermal states in $D=4$, ${\cal N}=4$ SYM at finite chemical and angular potential, thereby complementing and extending the results of [arXiv:1005.1287, arXiv:1806.01849, arXiv:1809.04084]. These solutions uplift to asymptotically AdS$_5 \times S^5$ solutions of Type IIB supergravity with equal angular momenta along AdS$_5$ ($J=J_1=J_2$) and $S^5$ ($Q=Q_1=Q_2=Q_3$). As we lower the mass $E$ at fixed $Q$ and $J$, the known Cveti\v{c}-L\"u-Pope (CLP) black holes are unstable to scalar condensation and the hairy black holes constructed here emerge as novel solutions associated to the instability. In the region of phase space where the CLP and hairy black holes coexist, the hairy black holes dominate the microcanonical ensemble and, therefore, describe a new thermodynamic phase of SYM. The hairy black holes extend beyond the CLP extremality surface all the way to the BPS surface, defined by $E = 3 Q + 2 J / L$. Through a combination of analytical and numerical techniques, we argue that the BPS limit of the hairy black holes is a singular, horizonless solution, and $not$ a new two-parameter family of BPS black holes that extend the known one-parameter Gutowski-Reall (GR) black hole solution, in contradiction with the conjectures of [arXiv:1005.1287, arXiv:1806.01849]. To further support our conclusions, we perform a near-horizon analysis of the BPS equations and argue that they do not admit any regular solutions with an horizon.