Logarithmic Corrections to Thermodynamics of Accelerating Black Holes

TL;DR

This work computes the leading low-temperature quantum corrections to the thermodynamics of four-dimensional accelerating black holes (Kerr, Reissner–Nordström, and Kerr–Newman) using the Euclidean path integral. Near extremality, the near-horizon region becomes (warped or twisted) AdS$_2\times$S$^2$, and the quantum corrections are dominated by zero modes associated with large diffeomorphisms and gauge transformations, yielding universal $\log T$ entropy contributions with coefficients set by the type and number of zero modes. For accelerating Kerr, RN, and Kerr–Newman black holes, the authors find $\delta S = \frac{3}{2}\log T$, $\delta S = \frac{5}{2}\log T$, and $\delta S = 2\log T$, respectively, reflecting the underlying near-horizon geometry and field content. The results illuminate how acceleration modifies the zero-mode structure and demonstrate a universal pattern: tensor-type graviton zero modes contribute $\frac{3}{2}\log T$, vector-type graviton and photon zero modes contribute $\frac{1}{2}\log T$ each, and these combine to give the total low-temperature quantum corrections to entropy in each case, with implications for the mass gap puzzle and black hole thermodynamics at very low temperatures.

Abstract

As pointed out in recent research, the near extremal black hole entropy with one-loop effect exhibits universal $\log T$ behaviour at sufficiently low temperature. In this paper, we discuss the low temperature quantum corrections to the thermodynamics of four dimensional accelerating black holes with rotation and charges by using the method of Euclidean path integral. The one-loop path integral for the black hole thermal partition function near extremality is dominated by zero modes defined with respect to the extremal background. For the accelerating black holes without rotation, the near horizon extremal geometry is a direct product of AdS$_2$ and S$^2$ with warping factors, and the gravitational zero modes contain both tensor and vector types, with the respective contributions to the near extremal black hole entropy being $(3/2)\log T$ and $(1/2)\log T$. While in the presence of rotation, the near horizon extremal geometry is a twist product of AdS$_2$ and S$^2$ and the gravitational vector modes are absent. For the accelerating black holes with charges, we also consider the one-loop path integral of the gauge field, where the photon zero modes are found to contribute an additional $(1/2)\log T$ term to the near extremal black hole entropy.