In this paper, we delve into the study of thermodynamics and phase transition of charged Gauss–Bonnet black holes within the context of anti-de Sitter space, with particular emphasis on the central charge’s role within the dual conformal field theory (CFT). We employ a holographic methodology that interprets the cosmological constant and the Newton constant as thermodynamic variables, leading to the derivation of a modified first law of thermodynamics that incorporates the thermodynamic volume and pressure. Our findings reveal that the central charge of the CFT is intrinsically linked to the variation of these constants, and its stability can be ensured by simultaneous adjustment of these constants. We further explore the phase structures of the black holes, utilizing the free energy. Our research uncovers the existence of a critical value of the central charge, beyond which the phase diagram displays a first-order phase transition between small and large black holes. We also delve into the implications of our findings on the complexity of the CFT. Our conclusions underscore the significant role of the central charge in the holographic thermodynamics and phase transition of charged Gauss–Bonnet black holes. Furthermore, we conclude that while the central charge considered provides suitable and satisfactory solutions for this black hole in 4 and 5 dimensions, it becomes necessary to introduce a unique central charge for this structure of modified gravity. In essence, the central charge in holographic thermodynamics is not a universal value and requires modification in accordance with different modified gravities. Consequently, the physics of the problem will significantly deviate from the one discussed in this article, indicating a rich and complex landscape for future work.

在本文中，我们深入研究反德西特空间背景下带电高斯-邦尼特黑洞的热力学和相变，特别强调中心电荷在双共形场理论（CFT）中的作用。我们采用全息方法将宇宙常数和牛顿常数解释为热力学变量，从而推导了包含热力学体积和压力的修正热力学第一定律。我们的研究结果表明，CFT 的中心电荷与这些常数的变化有着内在的联系，并且可以通过同时调整这些常数来确保其稳定性。我们利用自由能进一步探索黑洞的相结构。我们的研究揭示了中心电荷临界值的存在，超过该临界值，相图显示小黑洞和大黑洞之间的一阶相变。我们还深入研究了我们的发现对 CFT 复杂性的影响。我们的结论强调了中心电荷在带电高斯-邦尼特黑洞的全息热力学和相变中的重要作用。此外，我们得出的结论是，虽然所考虑的中心电荷为该黑洞在 4 维和 5 维中提供了合适且令人满意的解决方案，但有必要为这种修正重力结构引入独特的中心电荷。本质上，全息热力学中的中心电荷并不是一个普适值，需要根据不同的修正引力进行修正。 因此，该问题的物理原理将显着偏离本文讨论的物理原理，这表明未来工作的前景丰富而复杂。