Microscopic Theory of Black Hole Superradiance

TL;DR

This work provides a coherent microscopic account of black hole superradiance by analyzing extremal ergo-cold D1-D5-P black holes whose temperature vanishes while an ergosphere persists. The authors show that the superradiant frequency bound $0<\omega<m\Omega_H$ arises from Fermi-Dirac statistics of spin-carrying fermions in the dual CFT, and they derive this bound and the corresponding emission rates from both the gravity and CFT perspectives, finding agreement. They extend the analysis to four-dimensional cases and address the absence of superradiant linear-momentum emission, illustrating how the microscopic two-sector CFT structure encodes the ergoregion physics. The results illuminate the microphysical origin of superradiance in cold ergoregions and suggest a universal mechanism applicable to other extremal gravitating systems, with potential implications for extremal Kerr and related setups.

Abstract

We study how black hole superradiance appears in string microscopic models of rotating black holes. In order to disentangle superradiance from finite-temperature effects, we consider an extremal, rotating D1-D5-P black hole that has an ergosphere and is not supersymmetric. We explain how the microscopic dual accounts for the superradiant ergosphere of this black hole. The bound 0< omega < m Omega_H on superradiant mode frequencies is argued to be a consequence of Fermi-Dirac statistics for the spin-carrying degrees of freedom in the dual CFT. We also compute the superradiant emission rates from both sides of the correspondence, and show their agreement.

Figures (1)

• Figure 1: Four different kinds of black hole in the 'effective string' picture. The excitations of the two chiral sectors, with levels $L_0$ (left-moving) and $\bar{L}_0$ (right-moving), correspond to open strings attached to the brane bound state. (a) Supersymmetric static black hole: $L_0= 0$, $\bar{L}_0=N_R$: only the right-moving sector is excited. (b) Near-supersymmetric static black hole: $L_0=N_L> 0$, $\bar{L}_0=N_R> 0$. Left and right-moving excitations can annihilate to emit a closed string: this is Hawking radiation. (c) Supersymmetric rotating black hole: $L_0=0$, $\bar{L}_0=N_R-6 J_R^2/c> 0$. The coherent polarization of right-moving fermions yields a macroscopic (self-dual) angular momentum $J_R$. In the absence of left-moving open strings, there cannot be any radiation of closed strings, hence there is no Hawking nor superradiant emission. (d) Ergo-cold black hole: $L_0> 0$, and $\bar{L}_0=N_R-6 J_R^2/c= 0$ with $N_R >0$. The right-moving sector is a Fermi sea of polarized fermionic excitations, so the temperature vanishes. Open strings in this sector can interact with those in the left sector and emit closed strings that carry angular momentum: the black hole possesses a superradiant ergosphere. The superradiant bound on modes (\ref{['sradbound']}) is directly related to the energy of the Fermi level, and thus is a consequence of Fermi-Dirac statistics for the excitations of the CFT.