Abstract We study the phase structure and the microscopic interactions in regular Bardeen AdS black hole. The stable and metastable phases in the black hole are analysed through coexistence and spinodal curves. The solutions are obtained numerically as the analytic solution to the coexistence curve is not feasible. The P r − T r coexistence equation is obtained using a fitting formula. The coexistence and spinodal curves are plotted in P r − T r and T r − V r planes to explore the phase structure of the black hole. In the second part of our study, we were able to probe the microscopic interactions of regular Bardeen AdS black hole using the novel Ruppeiner geometry proposed by Wei et al. (2019). It is found that the microscopic interactions are not same in the small black hole (SBH) and large black hole (LBH) phases. In the SBH phase, there exists a repulsive interaction in the microstructure in the low temperature regime. In contrast, the microstructure associated with the LBH phase has attractive interaction throughout the parameter space. We found that, along the coexistence temperature both the SBH and LBH branches diverge to negative infinity with a critical exponent equal to 1 ∕ 2 .

中文翻译：

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反德西特时空规则巴丁黑洞的共存物理和微观结构

摘要 我们研究了常规 Bardeen AdS 黑洞的相结构和微观相互作用。通过共存和旋节线曲线分析黑洞中的稳定和亚稳定相。由于共存曲线的解析解是不可行的，因此这些解是通过数值获得的。使用拟合公式获得 P r - T r 共存方程。共存曲线和旋节线曲线绘制在 P r - T r 和 T r - V r 平面上，以探索黑洞的相结构。在我们研究的第二部分，我们能够使用 Wei 等人提出的新型 Ruppeiner 几何来探测常规 Bardeen AdS 黑洞的微观相互作用。(2019)。发现小黑洞（SBH）和大黑洞（LBH）相的微观相互作用是不同的。在 SBH 阶段，在低温状态下，微观结构中存在排斥相互作用。相比之下，与 LBH 相相关的微观结构在整个参数空间中具有吸引力的相互作用。我们发现，沿着共存温度，SBH 和 LBH 分支都发散到负无穷大，临界指数等于 1 ∕ 2 。