Thermodynamic law and holography dual of accelerating and rotating black hole in Nariai limit

TL;DR

This work analyzes accelerating and rotating black holes described by the rotating C-metric, focusing on thermodynamics and holography in the Nariai limit. It introduces a regularized Komar mass via background subtraction and derives a first law using the covariant phase space formalism, while also performing a 2D JT reduction to connect near-extremal dynamics to dilaton gravity. On the holographic side, it identifies a Kerr-CFT/Nariai-CFT structure with an extremal warped CFT description ($SL(2, ext{R}) imes U(1)$) and a hidden near-extremal $SL(2, ext{R}) imes SL(2, ext{R})$ symmetry, validating entropy through Cardy-type formulas. The JT reduction provides a consistent bridge between 4D thermodynamics and 2D holographic dynamics, supporting the proposed dualities, though the de Sitter context remains conceptually subtle and warrants further investigation.

Abstract

In this study, we investigate the thermodynamic law of accelerating and rotating black hole described by ro- tating C-metric, as well as holography properties in Nariai limit, which are related to Nariai-CFT and Kerr-CFT correspondence. In order to achieve this goal we define a regularized Komar mass with physical interpretation of varying the horizon area from spinless limit to general case, and derive the frist law based on this construction through covariant phase space formalism. Serving for potential future studies, we also reduce the model to a 2-dimensional JT-type action and discuss some of its properties.

Figures (4)

• Figure 1: The Penrose diagram for the global structure of C-metric in the case of $\theta=0$(left) and $0<\theta<\frac{\pi}{2}$ (right).
• Figure 2: The Penrose diagram for the global structure of C-metric in the case of $\theta=\frac{\pi}{2}$(left) and $\frac{\pi}{2}<\theta<\pi$ (right).
• Figure 3: Left:The three possible horizons under different parameters, where $f_{i}(r)=\frac{1}{3}\Lambda_i{} r^2(a^2+r^2)$, $g(r)=(r^2-2mr+a^2+e^2)(1-\alpha^2r^2)$, three different $\lambda$ correspond to one horizon, two degenerating horizons and three simple horizons in $r>0$ respectively. The possible conformal boundary is the dashed line. Right: The "global" diagram of rotating C-metric with positive cosmological constant, where thick red lines correspond to conformal infinity and thick black lines are degenerate boundaries for two overlapping atlas.
• Figure 4: The sketch map of the Cauchy slice and its subset $\Sigma$, in which the whole loop is $\partial \Sigma=(-S_{\mathcal{H}}) \cup (-S_{+}) \cup S_{-}\cup S_{\infty}$, and $\phi$ coordinate is suppressed.