In this paper, we have investigated the phase transition in black holes when Gauss–Bonnet corrections to the spacetime curvature and Born–Infeld extension in stress–energy tensor of electromagnetic field are considered in a negative cosmological constant background. It is evident that the black hole undergoes a phase transition as the specific heat capacity at constant potential shows discontinuities. Further, the computation of the free energy of the black hole, the Ehrenfest scheme and the Ruppeiner state space geometry analysis are carried out to establish the second order nature of this phase transition. The effect of non-linearity arising from Born–Infeld electrodynamics is also evident from our analysis. Our investigations are done in general D-spacetime dimensions with \(D>4 \), and specific computations have been carried out in \(D= 5,6,7\) spacetime dimensions.

在本文中，我们研究了在负宇宙学常数背景下考虑对电磁场的应力-能量张量中的时空曲率和Born-Infeld扩展进行高斯-邦尼特校正时，黑洞的相变。显然，黑洞经历了相变，因为在恒定电势下的比热容量显示出不连续性。此外，还进行了黑洞自由能的计算，埃伦菲斯特（Ehrenfest）方案和鲁珀纳（Ruppeiner）状态空间几何分析，以建立该相变的二阶性质。从Born-Infeld电动力学中产生的非线性效应也从我们的分析中显而易见。我们的研究是在一般的D-时空维度下完成的，其中\（D> 4 \），并且已在\（D = 5,6,7 \）时空维度中进行了具体计算。