Holographic complexity of hyperbolic black holes

We calculate the holographic complexity of a family hyperbolic black holes in an Einstein-Maxwell-dilaton system by applying $\text{complexity}=\text{action}$ conjecture. While people previously studied spherical same system, we show that have intriguing features. confirm expression mainly depends on spacetime causal structure despite rich thermodynamics. The nontrivial neutral limit exists only for enables us to analytically obtain growth rate during phase transitions. find dilaton accelerates complexity, and Lloyd bound can be violated. This is contrast case where dilation slows down, always satisfied. As special case, study hairy