Harvesting correlations in Schwarzschild and collapsing shell spacetimes

TL;DR

This paper investigates how two Unruh-DeWitt detectors can extract correlations from the vacuum state in a collapsing black hole spacetime, revealing the influence of different vacua and the horizon on correlation harvesting.

Contribution

It provides a detailed comparison of correlation harvesting in Vaidya and Schwarzschild spacetimes, highlighting the horizon's inhibitory effect and the vacuum-dependent correlation capacities.

Findings

Unruh vacuum closely matches Vaidya vacuum near the horizon.

All vacua inhibit correlations at the horizon.

Harvesting efficiency depends on detector signaling ability.

Abstract

We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spacetime and Schwarzschild spacetimes, and the detectors couple to the proper time derivative of the field. First we find that, with respect to the harvesting protocol, the Unruh vacuum agrees very well with the Vaidya vacuum near the horizon even for finite-time interactions. Second, all four vacua have different capacities for creating correlations between the detectors, with the Vaidya vacuum interpolating between the Unruh vacuum near the horizon and the Boulware vacuum far from the horizon. Third, we show that the black hole horizon inhibits \textit{any} correlations, not just entanglement. Finally, we show that the efficiency of the harvesting protocol depend strongly on the signalling ability of the detectors, which is highly non-trivial in presence of curvature. We provide an asymptotic analysis of the Vaidya vacuum to clarify the relationship between the Boulware/Unruh interpolation and the near/far from horizon and early/late-time limits. We demonstrate a straightforward implementation of numerical contour integration to perform all the calculations.