On Unitary Evolution of a Massless Scalar Field In A Schwarzschild Background: Hawking Radiation and the Information Paradox

TL;DR

This paper introduces a Hamiltonian formalism for a massless scalar field in Schwarzschild spacetime, demonstrating unitarity of evolution and providing insights into Hawking radiation, black hole entropy, and the information paradox.

Contribution

It presents a novel Hamiltonian approach that shows the unitarity of scalar field evolution in black hole backgrounds, offering new perspectives on longstanding paradoxes.

Findings

Unitarity of scalar field evolution in Schwarzschild background

Reinterpretation of Hawking radiation within the formalism

Implications for black hole entropy and information paradox

Abstract

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.