Abstract
The general form of the action growth for a large class of static black hole solutions in modified gravity which includes $F(R)$-gravity models is computed. The cases of black hole solutions with non vanishing Ricci curvature are also considered, generalizing the results previously found and valid only for constant curvature black holes. An argument is put forward to provide a physical interpretation of the results.
Highlights
Brown et al proposed an interesting conjecture in the anti–de Sitter (AdS)=CFT framework, according to which the quantum computational complexity of a holographic state may be inferred from the classical action related to a specific region in the bulk [1]
In this paper we have investigated the general form of the action growth for some modified gravity black hole solutions
By making use of the first law of BH thermodynamics in these modified gravity models, we have shown that the energy of our black holes is always proportional to the integration constant associated with the solution
Summary
Brown et al proposed an interesting conjecture in the AdS=CFT framework, according to which the quantum computational complexity of a holographic state may be inferred from the classical action related to a specific region in the bulk [1] Such a proposal has been checked in the context of the anti–de Sitter (AdS) black holes (BHs) in general relativity (GR), and this is an interesting test for the complexity/action (CA) duality [2]. Quite apart from computations, it is important to assess the validity of the conditions allowing us to restrict attention to spherically symmetric solutions beyond the obvious demand of simplicity and the advantage of working with exact solutions, and to relate the action grow with the physics of black hole evaporation In this context, the more important property is the grows being proportional to the internal energy of the black hole.
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