Abstract
Using the complexity=action framework, we compute the late time growth of complexity for charged black holes in Lovelock gravity. Our calculation is facilitated by the fact that the null boundaries of the Wheeler-DeWitt patch do not contribute at late times and essential contributions coming from the joints are now understood. The late time growth rate reduces to a difference of internal energies associated with the inner and outer horizons, and in the limit where the mass is much larger than the charge, we reproduce the celebrated result of 2M/π with corrections proportional to the highest Lovelock coupling in even (boundary) dimensions. We find in some cases a minimum mass below which complexity remains effectively constant, even if the black hole contains a nondegenerate horizon.
Highlights
The anti–de Sitter/conformal field theory (AdS/CFT) duality [1] has brought surprising insight to the nature of quantum gravity
Our calculation is facilitated by the fact that the null boundaries of the Wheeler-DeWitt patch do not contribute at late times and essential contributions coming from the joints are understood
We find in some cases a minimum mass below which complexity remains effectively constant, even if the black hole contains a nondegenerate horizon
Summary
Using the complexity 1⁄4 action framework, we compute the late time growth of complexity for charged black holes in Lovelock gravity. From the seminal works of Bekenstein [6,7] and Hawking and coworkers [8,9], the thermodynamic properties of black hole geometries have raised intriguing questions about the possible microscopic structure of black holes Understanding how these quantities are encoded in the dual CFT is presently an active area of study [10,11,12,13,14,15,16,17,18,19,20,21,22]. The CA proposal states that the complexity of the state is given by the Lorentzian action evaluated on the Wheeler-DeWitt (WDW) patch
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