Distinguishing Schwinger effect from Hawking radiation in Reissner-Nordstr{ö}m black holes via entanglement

TL;DR

The paper investigates how Hawking radiation and Schwinger pair production co-exist and intertwine in charged black holes, proposing entanglement entropy as a diagnostic tool. By applying the island formula to near-extremal Reissner–Nordström black holes, it computes the total radiation entropy, and by employing the heat-kernel method (along with brick-wall and Pauli–Villars regularization) isolates the entanglement entropy arising purely from the Schwinger effect. The results show that in near-extremal cases after the Page time, the Schwinger contribution dominates the entanglement entropy, while the Hawking part can be extracted as a difference; in the extremal limit, Hawking radiation vanishes and the entropy is governed solely by the Schwinger mechanism, albeit with regulator-sensitive subtleties. These findings highlight entanglement entropy as an effective handle to decouple the two mechanisms and suggest avenues for extending the analysis to rotating or AdS spacetimes and to spinor fields.

Abstract

A charged black hole can emit charged particles via two independent mechanisms: the Hawking radiation and the Schwinger effect, which are intertwined in the radiation spectrum. In this paper, we will show that the two effects can be distinguished by analyzing the entanglement entropy carried by the produced particle pairs. Explicitly, we apply the island formula to the near extremal Reissner-Nordstr{ö}m (RN) black hole to calculate the total entanglement entropy of the radiation. Meanwhile we use the heat kernel method to calculate the entanglement entropy of charged particle pairs produced solely from the Schwinger effect. By comparing with the total entanglement entropy, we obtain the entanglement entropy produced purely from the Hawking radiation. Consequently, the two effects are distinguishable in near extremal RN black holes after the Page time. Furthermore, we also employ the brick wall model and the Pauli-Villars regularization to derive the entanglement entropy from the Schwinger effect, which gives a slightly different result with that obtained from the heat kernel method.