Holographic complexity of the electromagnetic black hole

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In this paper, we use the "complexity equals action" (CA) conjecture to evaluate the holographic complexity in some multiple-horzion black holes for F(Riemann) gravity coupled to a first-order source-free electrodynamics.

• Motivated by the vanishing result of the purely magnetic black hole founded by Goto $et.\, al$, we investigate the complexity in a static charged black hole with source-free electrodynamics and find that this vanishing feature of the late-time rate is universal for a purely static magnetic black hole.
• However, this result shows some unexpected features of the late-time growth rate.
• We show how the inclusion of a boundary term for the first-order electromagnetic field to the total action can make the holographic complexity be well-defined and obtain a general expression of the late-time complexity growth rate with these boundary terms.