Black holes exert quantum pressure coming from the nonlocal gravity correction. We investigate this nonlocal correction for black holes in anti-de Sitter (AdS) spacetime and its dual boundary field theory. We show that the second order curvature and the nonlocal actions do not backreact on the AdS black hole metric. Thus, the interpretation of quantum pressure holds in the bulk for AdS black hole, generalizing the previous result for the asymptotically flat black hole. We then show that the leading geometric correction comes from the third order in curvature and explicitly calculate the corrections to the metric and to the horizon. For applications to AdS/CFT, we conjectured a nonlocal Gibbons–Hawking–York boundary term along with the necessary counter terms to cancel the ultraviolet divergence of the bulk action. We then calculate the thermodynamic quantities in the bulk and discuss their properties.

黑洞施加来自非局域引力校正的量子压力。我们研究了反德西特（AdS）时空中黑洞的非局域校正及其对偶边界场理论。我们证明二阶曲率和非局部作用不会对 AdS 黑洞度量产生反作用。因此，量子压力的解释对于 AdS 黑洞来说在很大程度上是成立的，概括了先前关于渐近平坦黑洞的结果。然后，我们表明主要的几何校正来自曲率的三阶，并显式计算对度量和地平线的校正。对于 AdS/CFT 的应用，我们推测了非局部吉本斯-霍金-约克边界项以及必要的反项，以消除体作用的紫外线发散。然后我们计算整体热力学量并讨论它们的性质。