General bounds on holographic complexity

A bstract We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal slice has nonnegative vacuum-subtracted volume, and vanishes if only spacetime is identically pure AdS. Under Complexity=Volume proposal, this constitutes holographic complexity theorem. The result features number of parallels with energy theorem, including assumption an condition that excludes false vacuum decay (the weak condition). Our proof rigorously established in broad generality four bulk dimensions, we provide strong evidence favor generalization to arbitrary dimensions. techniques also yield Lloyd’s bound class spacetimes. further establish partial rigidity wormholes: wormholes given throat size are more complex than AdS-Schwarzschild same size.