On the first law of holographic complexity
arXiv:1912.10436
Abstract
In this paper, we examine the proposed first law of holographic complexity through studying different perturbations around various spacetime backgrounds. We present a general expression for the variation of the holographic complexity on arbitrary backgrounds by an explicit covariant computation. Interestingly, the general expression can be written as a function of gravitational conserved charges reminiscent of the first law of thermodynamics.
24 pages,Some improvements, New appendixes, Some rearrangements: Section 2 is moved to appendix B, To appear in PRD