We investigate the cooling–heating phase transition of the Euler–Heisenberg-AdS black hole. First, the black hole thermodynamic quantities and the state equation are reviewed. Then, we research cooling–heating phase transition and further plot the inversion and isenthalpic curves in the T–P plane. Meanwhile, we find that the inversion temperature gradually decreases with the increase of Euler–Heisenberg parameter a for the inversion curves, while this parameter has no effect in the cooling region, and the isenthalpic curves gradually move to the positive direction of X-axis with the increase of Euler–Heisenberg parameter a in the heating region. In particular, the inversion temperature and pressure of this black hole are negative, we deem that this case is caused by the vacuum polarization and the quantum electrodynamics corrections, which makes the electromagnetic energy (repulsion force) produced by the black hole shield the gravity produced by the black hole mass. In addition, this explanation has been mentioned in previous studies [M. Daniela and B. Nora, Phys. Rev. D 102, 084011 (2020); R. Ruffini, Y. B. Wu and S. S. Xue, Phys. Rev. D 88, 085004 (2013)].

中文翻译：

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Euler-Heisenberg-AdS黑洞的冷却-加热相变

我们研究了 Euler-Heisenberg-AdS 黑洞的冷却-加热相变。首先，回顾了黑洞的热力学量和状态方程。然后，我们研究了冷却-加热相变，并进一步绘制了反演曲线和等焓曲线。吨–磷飞机。同时，我们发现随着欧拉-海森堡参数的增加，反演温度逐渐降低一种对于反演曲线，该参数在冷却区没有影响，等焓曲线逐渐向正方向移动X- 轴随着欧拉-海森堡参数的增加一种在加热区。特别是这个黑洞的反转温度和压力是负的，我们认为这种情况是由真空极化和量子电动力学校正引起的，这使得黑洞产生的电磁能（排斥力）屏蔽了产生的引力由黑洞质量。此外，这种解释在以前的研究中已经提到过[M. 丹妮拉和 B.诺拉，物理。牧师 D 102, 084011 (2020); R. Ruffini、YB Wu 和 SS Xue，物理。牧师 D 88, 085004 (2013)]。