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arXiv 2409.16248hep-thgr-qc
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从极远处看极端黑洞

Looking at extremal black holes from very far away

Maciej Kolanowski, Donald Marolf, Ilija Rakic, Mukund Rangamani, Gustavo J. Turiaci

AI总结:

本研究从完整高维渐近平坦/AdS几何视角出发,找到欧几里得引力二次涨落算符的离壳本征模,验证其是近极端黑洞量子效应的成因,同时解决了作用量符号不定性与旋转等距性模式的技术难题。

摘要:

近极端黑洞会受到显著的量子效应影响,这类效应会改变其低温热力学行为。迄今为止,学界分析这些量子效应时,都将几何结构划分为近视界区域及其外部区域。从完整的高维渐近平坦或AdS(反德西特)几何的视角来理解并复现这类修正,是学界的迫切需求。本文针对这一问题展开研究,填补了该领域的空白。具体而言,我们找到了欧几里得引力动力学的二次涨落算符的离壳本征模,其本征值随温度线性趋于零。我们在爱因斯坦-希尔伯特理论中的AdS内的BTZ黑洞与带双曲视界的中性黑洞,以及爱因斯坦-麦克斯韦理论中的带电黑洞场景下验证了这一结论。这些模式的显著特征是随松原频率呈线性标度,再加上当系统趋近极端状态时其波函数定域在视界附近的特性,表明它们正是引发上述量子效应的原因。我们提出了一种围道方案来处理欧几里得爱因斯坦-麦克斯韦作用量的符号不定性,并推导了该作用量以辅助我们的分析。我们还解决了与稳态黑洞时空中旋转等距性相关的模式的技术难题。

英文摘要:

Near-extremal black holes are subject to large quantum effects, which modify their low-temperature thermodynamic behavior. Hitherto, these quantum effects were analyzed by separating the geometry into the near-horizon region and its exterior. It is desirable to understand and reproduce such corrections from the full higher-dimensional asymptotically flat or AdS geometry's perspective. We address this question in this article and fill this gap. Specifically, we find off-shell eigenmodes of the quadratic fluctuation operator of the Euclidean gravitational dynamics, with eigenvalues that vanish linearly with temperature. We illustrate this for BTZ and neutral black holes with hyperbolic horizons in AdS in Einstein-Hilbert theory, and for the charged black holes in Einstein-Maxwell theory. The linear scaling with Matsubara frequency, which is a distinctive feature of the modes, together with the fact that their wavefunctions localize close to the horizon as we approach extremality, identifies them as responsible for the aforementioned quantum effects. We provide a contour prescription to deal with the sign indefiniteness of the Euclidean Einstein-Maxwell action, which we derive to aid our analysis. We also resolve a technical puzzle regarding modes associated with rotational isometries in stationary black hole spacetimes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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