Diving into a holographic superconductor

TL;DR

This paper explores the complex internal dynamics of holographic superconductors, revealing intricate behaviors such as Josephson oscillations and Kasner inversions near the black hole horizon, with results showing temperature-sensitive fractal patterns.

Contribution

It provides a detailed analysis of the interior spacetime of holographic superconductors, uncovering new phenomena like Kasner inversions and fractal behavior near critical temperatures.

Findings

Identification of Josephson oscillations in the condensate

Discovery of temperature-dependent Kasner inversions

Fractal-like behavior of Kasner exponents near critical temperatures

Abstract

Charged black holes in anti-de Sitter space become unstable to forming charged scalar hair at low temperatures $T < T_\text{c}$. This phenomenon is a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior. The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible 'Kasner inversions' in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity. Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on $T$, and diverges at a discrete set of temperatures $\{T_n\}$ that accumulate at $T_c$. Near these $T_n$, the final Kasner exponent exhibits fractal-like behavior.