A Simplified, Bohr Quantum Theoretical Derivation of the Unruh Temperature, Entropy, and Evaporation

Details A Simplified, Bohr Quantum Theoretical Derivation of the Unruh Temperature, Entropy, and Evaporation A Simplified, Bohr Quantum Theoretical Derivation of the Unruh Temperature, Entropy, and Evaporation

2010-11-04

arxiv.org/abs/1011.1473v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

seven pages, no figures

Scientific paper

In this work we reproduce Unruh temperature for a spherical physical system using a simplified rule, very similar to Bohr angular momentum quantization postulate interpreted via de Broglie relation, and using a thermal equilibrium stability condition. (Our rule, by a deeper analysis that goes over basic intentions of this work, corresponds, for Schwarzschild black hole, to a closed string loop theory of Copeland and Lahiri.) Firstly, we suppose that at the surface of a large system gravitational field of this system can generate some quantum excitations, i.e. small quantum systems. Mass spectrum of this small quantum system is determined using a rule that states that circumference of the large system holds integer numbers of the reduced Compton wavelengths of this small quantum system. Secondly, we suppose that absolute value of the classical gravitational interaction between large system and small quantum system in the ground state is equivalent to thermal kinetic energy of the small quantum system interacting with large system as thermal reservoir. It is very similar to virial theorem of the ideal gas and it yields directly and exactly Unruh temperature. Finally, using Unruh temperature and thermodynamical law, we originally propose corresponding Unruh entropy and Unruh evaporation of the system and demonstrate that for Schwarzschild black hole Unruh temperature, entropy and evaporation can be exactly reduced in the Hawking temperature, Bekenstein-Hawking entropy and Hawking evaporation.

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