We consider black hole solutions with electric and magnetic sources in the four-dimensional Einstein-Born-Infeld-AdS theory with spherical, planar and hyperbolic horizon geometries. Exact analytical solutions for the metric function, electric and magnetic fields were obtained and they recover the RN-AdS black hole in the limit \(\beta \rightarrow +\infty \) for spherical horizon in the absence of the magnetic charge. Expressions for temperature, electric and magnetic potential were obtained and they satisfy the first law of the extended black hole thermodynamics, where a negative cosmological constant is associated with thermodynamic pressure. Also, the Born-Infeld vacuum polarization term \(Bd\beta \) was included into the first law in order to satisfy the Smarr relation. Critical behavior of the black hole was examined and condition on electric and magnetic charges were obtained when phase transition appears. Also, the critical ratio and capacity at constant pressure were calculated. Electric and magnetic charges enter into the metric function and thermodynamic quantities symmetrically and thus the presence of the magnetic charge does not bring very significant new features. Finally, we examine the Joule-Thomson expansion if the black hole mass is fixed. The inversion and isenthalpic curves were plotted and the cooling and heating regions were demonstrated. These results recover the Joule-Thomson expansion recently considered for the RN-AdS black hole in the corresponding limit.

我们在具有球面、平面和双曲视界几何形状的四维爱因斯坦-出生-因菲尔德-AdS 理论中考虑了具有电源和磁源的黑洞解。获得了度量函数、电场和磁场的精确解析解，它们在没有磁荷的情况下恢复了球面视界极限\(\beta \rightarrow +\infty \) 中的 RN-AdS 黑洞。获得了温度、电势和磁势的表达式，它们满足扩展黑洞热力学第一定律，其中负宇宙常数与热力学压力相关。此外，Born-Infeld 真空极化项\(Bd\beta \)被纳入第一定律以满足 Smarr 关系。检查了黑洞的临界行为，并获得了出现相变时的电荷和磁荷条件。此外，还计算了恒压下的临界比和容量。电荷和磁荷对称地进入度量函数和热力学量，因此磁荷的存在不会带来非常显着的新特征。最后，如果黑洞质量是固定的，我们将检查焦耳-汤姆逊膨胀。绘制了反演和等焓曲线，并演示了冷却和加热区域。这些结果恢复了最近考虑的 RN-AdS 黑洞在相应极限中的焦耳-汤姆森扩展。