Extremal AdS Black Holes as Fluids: A Matrix Large-Charge EFT Approach

TL;DR

This paper introduces a matrix-valued large-charge effective field theory that models extremal AdS black holes as conformal fluids, successfully reproducing their thermodynamics and entropy through a fluid/gravity correspondence.

Contribution

It develops a novel matrix EFT approach for large-charge extremal AdS black holes, capturing their thermodynamics, boundary stress tensor, and entropy microscopically.

Findings

Exact reproduction of black hole thermodynamics and boundary stress tensor.

Explicit fluid solutions for rotating extremal black holes.

Microscopic mode-counting accounts for the entropy.

Abstract

We develop a simple, yet powerful, matrix-valued large-charge EFT that captures the thermodynamic behavior of rotating extremal large-charge AdS black holes. We introduce a minimal "matrix EFT" by promoting the complex scalar in large charge EFT to a complex $N\times N$ adjoint scalar, whose $O(N^2)$ modes contribute at zero temperature. Employing a mean-field approximation, we solve the self-consistency equations and obtain explicit rigidly rotating fluid solutions. We demonstrate that their energy, angular momenta, and charge densities exactly reproduce the thermodynamics and boundary stress tensor of zero-temperature conformal fluids. A microscopic mode-counting further accounts for the $O(N^2)$ entropy. Via the fluid/gravity correspondence, this fluid describes an extremal AdS black hole in large charge limit. We also comment on supersymmetric BPS black holes, which fall outside the usual hydrodynamic regime but nevertheless exhibit simple, universal behavior in the large angular momentum limit. In this regime, their non-linear charge-spin relations simplify to form reminiscent of our extremal fluid solutions at large angular momentum limit.