Adopting the Uncertainty Principle for the Entropy Estimation of Black Holes, de Sitter Space and Rindler Space

TL;DR

This paper uses the uncertainty principle to derive relationships between temperature and entropy for black holes, de Sitter space, and Rindler space, emphasizing the proportionality to surface gravity and area across different dimensions.

Contribution

It introduces a simple physical approach based on the uncertainty principle to estimate entropy and temperature for various spacetime horizons, extending to higher dimensions.

Findings

Entropy is proportional to surface area for black holes and de Sitter space.

Temperature relates to surface gravity in different spacetime contexts.

Results extend to higher-dimensional spaces.

Abstract

By a simple physical consideration and uncertain principle, we derive that temperature is proportional to the surface gravity and entropy is proportional to the surface area of the black hole. We apply the same consideration to de Sitter space and estimate the temperature and entropy of the space, then we deduce that the entropy is proportional to the boundary surface area. By the same consideration, we estimate the temperature and entropy in the uniformly accelerated system (Rindler coordinate). The cases in higher dimensions are considered.