The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer Approach

TL;DR

This paper investigates the quantum statistical entropy of a 5D Ricci-flat black string using an improved thin-layer method, revealing how extra-dimensional modes influence entropy in a semi-classical framework.

Contribution

It introduces a novel calculation of black string entropy incorporating extra-dimensional quantization and the thin-layer approach, extending understanding of higher-dimensional black objects.

Findings

Entropy is a linear sum of black hole and cosmological horizon areas.

Quantized modes in the extra dimension discretize the entropy proportionality coefficients.

Small-mass approximation is justified by large brane separation.

Abstract

In this paper, the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized by Randall-Sundrum mass relationship. We use the two-dimensional area to describe this black string's entropy which, in the small-mass approximation, is a linear sum of the area of the black hole horizon and the cosmological horizon. The proportionality coefficients of entropy are discretized with quantized extra dimensional modes. It should be noted that the small-mass approximation used in our calculation is naturally justified by the assumption that the two branes are located far apart.