Hidden conformal symmetry of the rotating charged AdS black holes in quadratic $f$($T$) gravity

TL;DR

This paper demonstrates that rotating charged AdS black holes in quadratic $f(T)$ gravity exhibit hidden conformal symmetry, allowing the derivation of their entropy via dual 2D CFTs, extending holographic duality beyond Kerr black holes.

Contribution

It extends the holographic correspondence to charged rotating AdS black holes in $f(T)$ gravity, showing their duality to 2D CFTs with matching entropy calculations.

Findings

Scalar wave equation reveals 2D conformal symmetry near the horizon.

Conformal symmetry is broken by azimuthal angle identification, leading to finite temperatures.

Microscopic CFT entropy matches Bekenstein-Hawking entropy for specific parameters.

Abstract

The nonextremal Kerr black holes have been considered to be holographically dual to two-dimensional (2D) conformal field theories (CFTs). In this paper, we extend the holography to the case of an asymptotically anti--de Sitter (AdS) rotating charged black holes in $f$($T$) gravity, where $f(T) = T + \alpha T^2$, where $\alpha$ is a constant. We find that the scalar wave radial equation at the near-horizon region implies the existence of the 2D conformal symmetries. We note that the $2\pi$ identification of the azimuthal angle $\phi$ in the black hole line element, corresponds to a spontaneous breaking of the conformal symmetry by left and right temperatures $T_{L}$ and $T_{R}$, respectively. We show that choosing proper central charges for the dual CFT, we produce exactly the macroscopic Bekenstein-Hawking entropy from the microscopic Cardy entropy for the dual CFT. These observations suggest that the rotating charged AdS black hole in $f$($T$) gravity is dual to a 2D CFT at finite temperatures $T_{L}$ and $T_{R}$ for a specific value of mass $M$, rotational, charge, and $f$($T$) parameters, $\Omega$, $Q$, and $|\alpha|$, respectively.