Thermodynamic relation on black branes with arbitrary cosmological constant

TL;DR

The paper investigates the universality of the Goon-Penco thermodynamic relation in $(n+1)$-dimensional black branes with an arbitrary cosmological constant, including configurations with both black-hole and cosmological horizons and descriptions in cylindrical coordinates. Using explicit topological dilaton black holes in de Sitter space and rotating black brane solutions in Einstein-Maxwell-dilaton gravity, the authors derive the relevant thermodynamic quantities and first-law relations, and show that the GP relation remains form-invariant under perturbations parameterized by $\eta$, across dimensions and coordinate choices. The results demonstrate that the GP relation is universal for spacetimes with multiple horizons and multiple extensive parameters, reinforcing its connection to the Weak Gravity Conjecture in quantum gravity and providing a practical method to study horizon coexistence in higher-dimensional settings. These findings generalize the GP framework to multi-parameter black branes and offer a pathway for future explorations of quantum gravity constraints in non-spherical and higher-dimensional spacetimes.

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.