Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS$_4$ Black Holes

Abstract

We comprehensively discuss various microscopic approaches to the Bekenstein-Hawking entropy for rotating, electrically charged, asymptotically AdS$_4$ non-extremal black holes in gauged supergravity. We apply the covariant phase space formalism to the near-horizon region to obtain a Cardy-formula-based microscopic explanation for the entropy, consistent with the Kerr/CFT correspondence. From the dual boundary CFT point of view, we estimate the free partition function in the matrix model approximation in the high-temperature regime and find qualitative agreement with the supergravity answer. All these different approaches match in the appropriate limits and support the universality of AdS black hole entropy even at high temperatures, far away from extremality. Prompted by the consistency of the results of statistical explanations for the AdS$_4$ black hole entropy, we discuss aspects of the rate of Hawking radiation at high temperatures from the CFT$_2$ perspective and found it to be universally proportional to the horizon area.

Figures (6)

• Figure 1: Three approaches to the universal result of asymptotically AdS rotating black holes
• Figure 2: The codimension-1 supersymmetric hypersurface (red plane) and the codimension-1 zero-temperature hypersurface (blue plane) in the parameter space; their intersection defines the BPS sector (black solid line).
• Figure 3: Numerical saddle-point solution to $\text{Re}(\rho(x))$ in which the range of $x$ is divided into 40, 60, 80, 100 segments, respectively. Accordingly, the normalization condition $\int^{100}_{-100} dx\rho(x)$ is approximated by discrete summations, and the result turns out to converge to $\int^{100}_{-100} dx\rho(x)=1.01858, 1.00804, 1.00297, 1.00000$, respectively.
• Figure 4: Numerical saddle-point solutions for the matrix model of ABJM free partition function on $S^2\times S^1$. We choose $k=1$, $\bar{\beta}=0.1$, $\lambda=0.3$, $\lambda_1=\lambda_2=\pi/2-0.2$, $\lambda_3=\lambda_4=\pi/2+0.2$. $\mu=10.7076$ is taken such that the normalization condition for the real part of the density of states $\int dx\rho(x)=1$ is satisfied.
• Figure 5: $\textrm{log}\, Z$ as a function of $Q$. We choose $k=1$, $T=10$, $\lambda=0.3$ and $a=0.9999$. The range of the integration variable $x$ is fixed to be $[-100,100]$. The blue and the red curves denote the results from gravity and the ABJM free partition function on $S^2\times S^1$, respectively.