Small Black String Thermodynamics

TL;DR

This paper investigates the thermodynamics of small black strings in four-dimensional spacetime with a negative cosmological constant, focusing on how small statistical fluctuations influence their stability and thermodynamic behavior.

Contribution

It introduces an analysis of small statistical fluctuations in black string thermodynamics and reveals their impact on stability and the equation of state.

Findings

Small fluctuations cause instability in small black strings.

Fluctuations significantly alter the equation of state.

Black string compressibility is inversely related to fluctuation parameter.

Abstract

We consider a cylindrically symmetric solution for the field equations of Einstein-Hilbert action with a negative cosmological constant in four dimensions. The small statistical fluctuation in the equilibrium thermodynamics of the black string solution is investigated. The small black string under the influence of small statistical fluctuation also follows the first law of thermodynamics. The behaviour of equation of states for black string changes significantly due to the fluctuation. The fluctuation causes instability to the small-sized black string only. Assuming the black string is fluid, the compressibility of the black string is inversely proportional to the fluctuation parameter.