Entanglement degradation in multi-event horizon spacetimes

TL;DR

This paper studies how quantum entanglement behaves in Schwarzschild-de Sitter black hole spacetimes, revealing that entanglement can increase with temperature under certain conditions, contrasting with typical degradation observed elsewhere.

Contribution

It introduces a novel analysis of entanglement in a spacetime with dual horizons, showing entanglement can increase with temperature, unlike in standard black hole scenarios.

Findings

Entanglement degrades with increasing Hawking temperature in standard scenarios.

In the Schwarzschild-de Sitter spacetime, entanglement increases with black hole temperature.

Entanglement remains robust or even enhances despite high temperatures.

Abstract

We investigate the degradation of quantum entanglement in the Schwarzschild-de Sitter black hole spacetime, by studying the mutual information and the logarithmic negativity for maximally entangled, bipartite states for massless minimal scalar fields. This spacetime is endowed with a black hole as well as a cosmological event horizon, giving rise to particle creation at two different temperatures. We consider two independent descriptions of thermodynamics and particle creation in this background. The first involves thermal equilibrium of an observer with either of the horizons. We show that as of the asymptotically flat/anti-de Sitter black holes, in this case the entanglement or correlation degrades with increasing Hawking temperatures. The second treats both the horizons combined in order to define a total entropy and an effective equilibrium temperature. We present a field theoretic derivation of this effective temperature and show that unlike the usual cases, the particle creation does not occur here in causally disconnected spacetime wedges but instead in a single region. Using the associated vacua, we show that in this scenario the entanglement never degrades but increases with increasing black hole temperature and holds true no matter how hot the black hole becomes or how small the cosmological constant is. We argue that this phenomenon can have no analogue in the asymptotically flat/anti-de Sitter black hole spacetimes.