A simplified quantum theoretical derivation of the Unruh and Hawking temperature

TL;DR

This paper presents a simplified quantum derivation of the Unruh temperature, linking it to classical gravitational potential energy, and extends the approach to analyze related thermodynamic properties like entropy.

Contribution

It introduces a novel, simplified method to derive the Unruh temperature without detailed quantum gravity, using classical gravitational potential energy and quantum systems.

Findings

Derived the Unruh temperature from classical gravitational potential energy.

Extended the formalism to calculate entropy and other thermodynamic characteristics.

Provided a simplified, understandable approach to quantum effects in gravity.

Abstract

In this work we suggest a sufficiently simple for understanding "without knowing the details of the quantum gravity" and quite correct deduction of the Unruh temperature (but not whole Unruh radiation process!). Firstly, we shall directly apply usual consequences of the Unruh radiation and temperature at surface gravity of a large spherical physical system and we shall show that corresponding thermal energy can be formally quite correctly presented as the potential energy absolute value of the classical gravitational interaction between this large and a small quantum system with well defined characteristics. Secondly, we shall inversely "postulate" small quantum system with necessary well defined characteristics and then, after "supposition" on the equivalence between potential energy absolute value of its gravitational interaction with large system with thermal energy, we shall obtain exact value of the Unruh temperature. Moreover, by very simple and correct application of suggested formalism (with small quantum system) at thermodynamic laws, we shall successfully study other thermodynamic characteristics, especially entropy, characteristic for Unruh and Hawking radiation