Entanglement in a model for Hawking radiation: An Application of Quadratic Algebras

TL;DR

This paper uses quadratic algebra models to exactly analyze entanglement and long-term behavior in a black hole system with Hawking radiation, revealing insights into radiation modifications and superradiance phenomena.

Contribution

It introduces a novel application of quadratic polynomially deformed algebras to model black hole radiation and entanglement dynamics exactly.

Findings

Exact calculation of bipartite entanglement entropies.

Insights into long-time behavior and modifications of Hawking radiation.

Observation of superradiance phenomena analogous to atomic Dicke superradiance.

Abstract

Quadratic polynomially deformed $su(1,1)$ and $su(2)$ algebras are utilised in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of a) infalling plus outgoing modes and b) black hole modes plus the infalling modes,using the Janus-faced nature of the model.The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Lastly, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance.