标题： BTZ黑洞在f(R,φ)引力中的热力学几何分析 显示英文标题

标题： Thermodynamic geometric analysis of BTZ black hole in f(R,φ) Gravity

摘要： 在本工作中，我们得到了f(R)引力下扩展黑洞解的热力学几何。 这是我们工作的基础。 我们还得到了一些解的f(R)模型的精确形式。 在热力学分析中，我们计算了这些解的温度和熵等热力学量，并将其与相应的BTZ黑洞进行比较。 之后，我们研究了Ruppeiner几何，如BTZ黑洞的f(R)-引力（扩展黑洞解），并分析了Ruppeiner几何与范德瓦尔斯方程在其相变过程中的热力学比较。 显示英文摘要

摘要： In this work, we obtain the thermodynamic geometry of the extended black hole solution under f(R) gravity. This is the foundation of our work. We also obtain the exact form of the f(R) model for some solutions. In the thermodynamic analysis, we calculate the thermodynamic quantities such as temperature and entropy of these solutions and compare them with the corresponding BTZ black holes. After that, we study the Ruppeiner geometry, such as the f(R)-gravity (extended black hole solution) of the BTZ black hole, and analyze the thermodynamic comparison of the Ruppeiner geometry with the van der Waals equation for its phase transition process.