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arXiv · 1702.06766

Action growth of charged black holes with a single horizon

Rong-Gen Cai·Misao Sasaki·Shao-Jiang Wang
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Abstract

According to the conjecture "complexity equals action," the complexity of a holographic state is equal to the action of a Wheeler-DeWitt (WDW) patch of black holes in anti-de Sitter space. In this paper we calculate the action growth of charged black holes with a single horizon, paying attention to the contribution from a spacelike singularity inside the horizon. We consider two kinds of such charged black holes: one is a charged dilaton black hole, and the other is a Born-Infeld black hole with $\beta^2 Q^2<1/4$. In both cases, although an electric charge appears in the black hole solutions, the inner horizon is absent, instead a spacelike singularity appears inside the horizon. We find that the action growth of the WDW patch of the charged black hole is finite and satisfies the Lloyd bound. As a check, we also calculate the action growth of a charged black hole with a phantom Maxwell field. In this case, although the contributions from the bulk integral and the spacelike singularity are individually divergent, these two divergences just cancel each other and a finite action growth is obtained. But in this case, the Lloyd bound is violated as expected.

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Rong-Gen Cai, Misao Sasaki, Shao-Jiang Wang. 2017-02-22. Action growth of charged black holes with a single horizon. https://doi.org/10.1103/physrevd.95.124002

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