Breaking of the universal nature of the central charge criticality in AdS black holes in Gauss-Bonnet gravity

Abstract

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in $D$-dimensional anti--de Sitter (AdS) spacetime. Here, the cosmological constant ($\mathrm{\ensuremath{\Lambda}}$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\ensuremath{\alpha}$) 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 utilizing 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 Cong et al. [Phys. Rev. Lett. 127, 091301 (2021)]. We observe that this universal nature breaks when such a 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 Kastor et al. [Classical Quantum Gravity 27, 235014 (2010)] 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 behavior 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.

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