The Hawking temperature, the uncertainty principle and quantum black holes

TL;DR

This paper offers a straightforward heuristic derivation of Hawking temperature using the Heisenberg uncertainty principle, clarifying its physical meaning and serving as educational material.

Contribution

It provides a simple, heuristic derivation of Hawking temperature that aligns with the original result, enhancing understanding and pedagogical utility.

Findings

Derivation matches Hawking's original temperature

Clarifies physical interpretation of Hawking radiation

Useful as educational resource in physics courses

Abstract

In 1974, Stephen Hawking theoretically discovered that black holes emit thermal radiation and have a characteristic temperature, known as the Hawking temperature. The aim of this paper is to present a simple heuristic derivation of the Hawking temperature, based on the Heisenberg uncertainty principle. The result obtained coincides exactly with Hawking's original finding. In parallel, this work seeks to clarify the physical meaning of Hawking's discovery. This article may be useful as pedagogical material in a high school physics course or in an introductory undergraduate physics course.