On the first law of holographic complexity
S. Sedigheh Hashemi, Ghadir Jafari, Ali Naseh
TL;DR
This paper investigates the first law of holographic complexity by deriving a covariant expression for its variation across different spacetime backgrounds, linking it to gravitational conserved charges similar to thermodynamic laws.
Contribution
It provides a general covariant formula for the variation of holographic complexity applicable to arbitrary backgrounds, connecting it to gravitational conserved charges.
Findings
Derived a covariant expression for complexity variation
Linked complexity variation to gravitational conserved charges
Applicable to various spacetime backgrounds
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.
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