Rescuing a black hole in the large-$q$ coupled SYK model

TL;DR

This paper develops an effective theory for coupled SYK models with time-dependent coupling, exploring a 'rescued black hole' scenario that transitions from an eternal black hole to a vacuum, revealing limitations of low-energy holographic descriptions.

Contribution

It introduces a large-$q$ effective theory for coupled SYK models with dynamic coupling and analyzes the holographic dual of a black hole rescue process.

Findings

The large-$q$ theory matches low-energy results in early rescue stages.

Deviations grow if rescue occurs late, indicating low-energy theory limitations.

Evidence suggests the bulk effective theory fails near the black hole's inner horizon.

Abstract

In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-$q$ theory with the bulk low energy effective theory. In particular, we study the special case of a ``rescued black hole'', which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS$_2$ vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-$q$ and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.