{"title":"灰色星系作为Kerr-AdS超辐射不稳定性的一个端点","authors":"Seok Kim, Suman Kundu, Eunwoo Lee, Jaeha Lee, Shiraz Minwalla, Chintan Patel","doi":"10.1007/jhep11(2023)024","DOIUrl":null,"url":null,"abstract":"A bstract Kerr-AdS d +1 black holes for d ≥ 3 suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) — a new class of coarse-grained solutions to Einstein’s equations which we construct in d = 3. Grey Galaxies are made up of a black hole with critical angular velocity ω = 1 in the ‘centre’ of AdS, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of AdS at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth ‘black hole’ contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large N limit. We also construct another class of solutions with the same charges; ‘Revolving Black Holes (RBHs)’. RBHs are macroscopically charged SO( d, 2) descendants of AdS-Kerr solutions, and consist of ω = 1 black holes revolving around the centre of AdS at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. 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引用次数: 7
摘要
d≥3的抽象Kerr-AdS d +1黑洞在极值以上的质量范围内具有经典超辐射不稳定性。我们推测,这些不稳定性会沉淀到灰色星系(gg)中——这是我们在d = 3中构造的爱因斯坦方程的一类新的粗粒度解。灰色星系是由一个临界角速度为ω = 1的黑洞组成的,黑洞位于AdS的“中心”,周围是一个巨大的扁平热块状气体盘,以光速围绕AdS中心旋转。气体携带的总能量的有限部分,因为它的参数低能量密度和大半径成反比。黑洞存在的质量一直延伸到统一界。它们的热力学是Kerr-AdS黑洞和大量气体弱相互作用的混合物。它们的边界应力张量是平滑的“黑洞”贡献和峰值气体贡献的总和,峰值气体贡献是在大N极限下边界球赤道附近的三角函数。我们还构造了另一类具有相同电荷的解;旋转黑洞(RBHs)。RBHs是AdS- kerr解的宏观带电SO(d, 2)后代,由ω = 1的黑洞组成,它们以固定的径向位置围绕AdS中心旋转,但在角方向上以量子波函数旋转。相对于GG解,RBH解在熵上是次要的,并且不构成超辐射不稳定性的终点。尽管如此,我们认为这些解的超对称版本对超对称态的谱有有趣的含义,例如$$ \mathcal{N} $$ N = 4 Yang-Mills理论。
Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability
A bstract Kerr-AdS d +1 black holes for d ≥ 3 suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) — a new class of coarse-grained solutions to Einstein’s equations which we construct in d = 3. Grey Galaxies are made up of a black hole with critical angular velocity ω = 1 in the ‘centre’ of AdS, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of AdS at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth ‘black hole’ contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large N limit. We also construct another class of solutions with the same charges; ‘Revolving Black Holes (RBHs)’. RBHs are macroscopically charged SO( d, 2) descendants of AdS-Kerr solutions, and consist of ω = 1 black holes revolving around the centre of AdS at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. $$ \mathcal{N} $$ N = 4 Yang-Mills theory.
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