Testing Holographic Conjectures of Complexity with Born-Infeld Black Holes

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In this paper, we use Born-Infeld black holes to test two recent holographic conjectures of complexity, the "Complexity = Action" (CA) duality and "Complexity = Volume 2.0" (CV) duality.

• The complexity of a boundary state is identified with the action of the Wheeler-deWitt patch in CA duality, while this complexity is identified with the spacetime volume of the WdW patch in CV duality.
• In particular, we check whether the Born-Infeld black holes violate the Lloyd bound: $\mathcal{\dot{C}\leq}\frac{2}{\pi\hbar}\left[ \left( M-Q\Phi\right) -\left( M-Q\Phi\right) _{\text{gs}}\right] $, where gs stands for the ground state for a given electrostatic potential.
• We find that the ground states are either some extremal black hole or regular spacetime with nonvanishing charges.