黑洞热力学的变分原理：渐近圆锥背景
Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds
摘要：
引力理论的变分问题与黑洞热力学直接相关。对于渐近局部AdS背景，已知全息重整化导致在理论的局部渐近对称下边界数据的等价类方面的变分原理，其自动导致满足热力学热力学第一定律的有限守恒电荷。我们表明，这种连接持有远远超出渐近AdS黑洞。特别是，我们制定的变分问题$\mathcal{N}=2$ STU超引力在四维边界条件相应的所谓的“减几何”服从。我们发现，这样的边界条件可以施加协变的一组渐近第二类约束，我们推导出适当的边界条件，使变分问题以及在两个不同的对偶框架的STU模型。这使我们能够定义有限的保守电荷与任何渐近Killing矢量，并证明这些费用满足Smarr公式和热力学热力学第一定律。此外，通过将理论提升到5维，然后在2-球上进行约化，我们提供了减几何和BTZ黑洞的热力学观测值之间的精确映射。表面项在这种识别中起着至关重要的作用。
英文摘要：
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification.
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