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

TL;DR

This paper demonstrates how to differentiate Hawking radiation from the Schwinger effect in charged black holes by analyzing entanglement entropy using multiple theoretical methods, revealing distinguishable signatures after the Page time.

Contribution

The study introduces a novel approach to distinguish Hawking radiation from the Schwinger effect in near extremal Reissner-Nordstr{"o}m black holes through entanglement entropy analysis using various computational techniques.

Findings

Hawking and Schwinger effects produce distinguishable entanglement entropy signatures.

The island formula effectively isolates the entanglement entropy from Hawking radiation.

Different regularization methods yield slightly different entanglement entropy results.

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{\"o}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.