Thermodynamic relation on rotating charged black strings with arbitrary cosmological constant

TL;DR

This paper demonstrates that the Goon-Penco relation, originally studied in spherically symmetric spacetimes, also holds universally for rotating charged black strings with arbitrary cosmological constants in cylindrical coordinates.

Contribution

It extends the validity of the Goon-Penco relation to non-spherically symmetric spacetimes, specifically rotating charged black strings with any cosmological constant.

Findings

GP relation retains its form in cylindrical coordinates

GP relation is valid for non-spherical spacetimes

Universal applicability of GP relation regardless of coordinate system

Abstract

The Goon-Penco (GP) relation was investigated on rotating charged black strings with an arbitrary cosmological constant. It has been demonstrated that the GP relation retains its form in the context of spacetimes described by cylindrical coordinates. In addition, the GP relation is derived in scenarios where the energy state parameters (including angular momentum $J$ and charge $Q$, etc.) are expressed as functions of the perturbation parameter $\eta$. This finding indicates that the GP relation is not only valid for spacetimes described by spherically symmetric coordinates, but also prevalent for non-spherically symmetric spacetimes, such as cylindrical coordinates. Therefore, the present study demonstrated that the GP relation is universal for spacetimes with arbitrary cosmological constants, irrespective of the adopted coordinate system.