Holographic complexity of Born–Infeld black holes

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.

Holographic complexity for nonlinearly charged Lifshitz black holes

“…where μ and Ω are black hole chemical potential and angular velocity, J and Q are black hole angular momentum and electric charge, '+' and '−' stand for outer horizon and inner horizon of the black hole, respectively. The validity of this upper bound in different types of black hole have been checked in many literatures [25][26][27][28][29][30][31]. However, there also have many cases that violate the Lloyd bound [32][33][34].…”

Holographic complexity for nonlinearly charged Lifshitz black holes

“…where µ and Ω are black hole chemical potential and angular velocity, J and Q are black hole angular momentum and electric charge, "+" and "-" stand for outer horizon and inner horizon of the black hole, respectively. The validity of this upper bound in different types of black hole have been checked in many literatures [25][26][27][28][29][30][31]. However, there also have many cases that violate the Lloyd bound [32][33][34].…”

Complexity Conjecture of Regular Electric Black Holes

“…Cai, et.al proved that the so-called Lloyd bound should be modified for charges or rotating black holes [14]. Although there are many cases of black holes that confirm the mentioned upper bound [15][16][17][18][19][20][21], its validity is an open question since there are different types of black hole violating the Lloyd bound [22][23][24]. Accordingly, the validity of CV and CA conjectures and their possible modifications deserve further study.…”