Kapec Daniel, Sheta Ahmed, Strominger Andrew, Toldo Chiara
Center for the Fundamental Laws of Nature, <a href="https://ror.org/03vek6s52">Harvard University</a>, Cambridge, Massachusetts 02138, USA.
Harvard Center of Mathematical Sciences and Applications, <a href="https://ror.org/03vek6s52">Harvard University</a>, Cambridge, Massachusetts 02138, USA.
Phys Rev Lett. 2024 Jul 12;133(2):021601. doi: 10.1103/PhysRevLett.133.021601.
Recent work has shown that loop corrections from massless particles generate 3/2logT_{Hawking} corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS_{2}×S^{2}, the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This "not-NHEK" geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits 3/2logT_{Hawking} behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.
近期的研究表明，无质量粒子的圈修正会对黑洞熵产生3/2logT霍金修正，这在冷近极端带电黑洞的热力学中占主导地位。在此，我们将此分析应用于近极端克尔黑洞。与AdS₂×S²一样，近视界极端克尔（NHEK）度规有一族可归一化的零模，对应于边界时间的重新参数化。对这些零模的路径积分在欧几里得NHEK配分函数的一圈近似中导致红外发散。我们通过在NHEK标度极限中保留主导的有限温度修正来调节这种发散。这种“非NHEK”几何提升了零模的本征值，使路径积分在红外区域有限。量子修正的近极端熵呈现出史瓦西模型特有的3/2logT霍金行为，并预测极端克尔黑洞的基态简并度会提升。
