Abstract
In this paper, according to CA duality, we study complexity growth of Born–Infeld (BI) black holes. As a comparison, we study action growth of dyonic black holes in Einstein–Maxwell gravity at the beginning. We study action growth of electric BI black holes in dRGT massive gravity, and find BI black holes in massive gravity complexify faster than the Einstein gravity counterparts. We study action growth of the purely electric and magnetic Einstein–Born–Infeld (EBI) black holes in general dimensions and the dyonic EBI black holes in four-dimensions, and find the manners of action growth are different between electric and magnetic EBI black holes. In all the gravity systems we considered, we find action growth rates vanish for the purely magnetic black holes, which is unexpected. In order to ameliorate the situation, we add the boundary term of matter field to the action and discuss the outcomes of the addition.
Highlights
Holographic principle relates boundary CFT to bulk theory of gravity, through the correspondence one can study the problems of strong coupling CFT on the boundary through studying weak coupling gravity in the bulk
The authors of Refs. [46,47,48] found that, action growth rates vanish for purely magnetic black holes in four dimensions
We have f (r ) − f(r ) < 0 for fixed mass and charge parameters, which implies r− < r− and r+ > r+ (r± are the inner and outer horizosn of the Einstein–Born– Infeld (EBI) black hole (45)), i.e., action growth rates of the double-horizoned BI black holes in Einstein massive gravity are superior to the ones of the Einstein gravity counterparts too, just as the lower two plots in Fig. 2 show us
Summary
Holographic principle relates boundary CFT to bulk theory of gravity, through the correspondence one can study the problems of strong coupling CFT on the boundary through studying weak coupling gravity in the bulk. It is natural to study complexity growth of black holes in different gravity systems to examine CA duality and Lloyd’s bound. We intend to study complexity growth of BI black holes, since we are interested in the effects of nonlinearity of BI theory on complexity growth. Since the magnetic black holes have been studied rarely, in this paper we will pay much attention to the magnetic black holes, and make a comparison of the effects between electric and magnetic charges on action growth. We are interested in studying action growth of BI black holes in massive gravity and study the effects of graviton mass. We add the boundary term of matter field proper to the gravity systems we considered and discuss the outcomes of the addition of the boundary term.
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