Revealing the interior of black holes out of equilibrium in the SYK model

TL;DR

This paper demonstrates how partial measurements and negative-energy perturbations in the SYK model can partially reveal black hole interiors, showing a proportional relationship between measurement extent, energy perturbation, and interior exposure.

Contribution

It introduces a method to partially expose black hole interiors in the SYK model through controlled perturbations and measurements, extending previous work on full exposure.

Findings

Partial measurements can reveal black hole interiors proportionally.

Weaker perturbations cause inward horizon shifts, exposing parts of the interior.

The boundary radiation burst correlates with measurement size and energy perturbation.

Abstract

The Sachdev-Ye-Kitaev (SYK) model can be used to describe black holes (BHs) in two-dimensional nearly-anti-de-Sitter gravity. We show that when such BHs are perturbed by a time-dependent negative-energy perturbation, their interior can be partially revealed. In the SYK model, a partial measurement of the state of the Majorana fermion pairs allows one to construct a matching time-dependent negative-energy perturbation of the BH geometry that shifts the state of the BH away from its equilibrium state. Kourkoulou and Maldacena showed that, if the perturbation is strong enough, the interior can be fully exposed and the BH disappears. Here, we show that when the perturbation is weaker than the threshold for full exposure, it effectively moves the horizon of the BH inwards, thus partially exposing the interior of the BH and leaving behind a smaller BH. The exposure is in proportion to the number of measured Majorana pairs and so also in proportion to the magnitude of the energy of the perturbation. From the boundary, the partial measurement is perceived as a burst of radiation whose strength and duration are proportional to the number of measured Majorana pairs.