Hawking Radiation, Entanglement Entropy, and Information Paradox of Kerr Black Holes

TL;DR

This paper investigates the information paradox in Kerr black holes by analyzing Hawking radiation and entanglement entropy, proposing a new resolution that aligns with quantum information theory and derives the Page curve microscopically.

Contribution

It introduces a novel resolution to the Kerr black hole information paradox by tracking ingoing Hawking quanta as a quantum wormhole and deriving the Page curve microscopically.

Findings

Consistent calculation of Hawking radiation rate using gravity and conformal field theory.

Formulation of the information paradox based on entanglement entropy evolution.

Derivation of the Page curve as a time-delay effect matching semi-classical results.

Abstract

The black hole information paradox is a long-standing problem in theoretical physics. Despite some recent progress, many issues remain open and should be clarified. In this paper, we study the information paradox of Kerr black holes and propose a new resolution with precise physical meanings. We compute the time-dependent Hawking radiation rate during the Kerr black hole evaporation using both the gravity and the conformal field theory approaches. Based on the consistent result from both approaches, we formulate the information paradox on top of the time evolution of the entanglement entropy between a Kerr black hole and its Hawking radiation quanta. To resolve the information paradox, we carefully keep track of the ingoing Hawking quanta through the Kerr black hole as a quantum wormhole and microscopically derive the Page curve as a time-delay effect. The result matches the previously obtained semi-classical Page curve and has a natural interpretation in quantum information theory.