Quantum and higher curvature corrections to the anti-de Sitter black hole

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.