Breaking of universal nature of central charge criticality in $AdS$ black holes in Gauss-Bonnet Gravity

TL;DR

This paper investigates how the universal behavior of the central charge at black hole phase transitions in AdS spacetime is affected by Gauss-Bonnet gravity and dimensionality, revealing that such universality breaks down in higher dimensions.

Contribution

It demonstrates the breaking of the universal critical central charge in Gauss-Bonnet gravity and higher dimensions, extending the understanding of black hole thermodynamics and phase transitions.

Findings

Universal critical central charge exists in 4D AdS black holes.

This universality breaks in 5D AdS black holes, even without Gauss-Bonnet terms.

Modified thermodynamic volume and phase structure are analyzed in higher dimensions.

Abstract

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($\Lambda$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\alpha$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this universal nature breaks when such phase transition is considered for black holes in the Gauss-Bonnet gravity. Apart from this, treating the Gauss-Bonnet parameter as a thermodynamic variable as suggested in \cite{kastori} in light of the consistency between first law and the Smarr relation leads to modified thermodynamic volume (conjugate to variable cosmological constant), adding to a new understanding of the Van der Waals gas like behaviour of the black holes in higher dimensional and higher curvature gravity theories. Our analysis considers a general $D$ dimensional background. We have then imposed a greater focus in the analysis of the phase structure of the five dimensional Gauss-Bonnet spacetime. Our analysis also shows that the general universal nature of the critical value of the central charge (which was present in four dimensional $AdS$ spacetime), breaks down in case of five dimensional $AdS$ spacetime even in the absence of Gauss-Bonnet gravity. This finding indicates the universal nature of the central charge may be a special feature of the four dimensional $AdS$ spacetime only.