Thermodynamic relation on black branes with arbitrary cosmological constant

TL;DR

This paper demonstrates that the Goon-Penco relation is universally valid across various dimensions and horizon types for black branes with any cosmological constant, confirming its broad applicability.

Contribution

It establishes the universal validity of the Goon-Penco relation for (n+1)-dimensional black branes with arbitrary cosmological constants across all horizon states.

Findings

GP relation preserved in various dimensions

Universal across event and cosmological horizons

Valid for arbitrary cosmological constants

Abstract

We investigated the Goon-Penco(GP) relationship in (n+1)-dimensional black branes with an arbitrary cosmological constant. Our analysis revealed that the GP relation preserved its form in four-dimensional and (n+1)-dimensional spacetimes, demonstrating its universal behavior with respect to dimensionality. Furthermore, we established that the GP relation exhibits universality across all states of the black hole, including those associated with the event horizon and the cosmological horizon. These findings confirm that the GP relationship remains valid for (n+1)-dimensional black holes and black branes with an arbitrary cosmological constant, independent of the coordinate system employed.