In this paper, the new formalism of thermodynamic geometry proposed in Hosseini Mansoori and Mirza (2019) is employed in investigating phase transition points and the critical behavior of a Gauss–Bonnet-AdS black hole in four dimensional spacetime. In this regard, extrinsic and intrinsic curvatures of a certain kind of hypersurface immersed in the thermodynamic manifold contain information about stability/instability of heat capacities. We, therefore, calculate the intrinsic curvature of the $Q$-zero hypersurface for a four-dimensional neutral Gauss Bonnet black hole case in the extended phase space. Interestingly, intrinsic curvature can be positive for small black holes at low temperature, which indicates a repulsive interaction among black hole microstructures. This finding is in contrast with the five-dimensional neutral Gauss Bonnet black hole with only dominant attractive interaction between its microstructures.

在本文中，Hosseini Mansoori和Mirza（2019）提出的热力学几何学的新形式主义被用于研究二维时空中的相变点和高斯-邦纳特-AdS黑洞的临界行为。在这方面，浸入热力学歧管中的某种超表面的外在和固有曲率包含有关热容量的稳定性/不稳定性的信息。因此，我们计算出$问$-零超曲面，用于扩展相空间中的四维中性高斯帽黑洞情况。有趣的是，内在曲率对于低温下的小黑洞可能为正，这表明黑洞微结构之间存在排斥相互作用。该发现与五维中性高斯帽黑洞相反，该黑洞在其微结构之间仅具有主要的吸引力相互作用。