Holographic complexity and action growth in massive gravities

Abstract: In this paper, we investigate the growth rates of action for the anti-de Sitter black holes in massive-Einstein gravity models and obtain the universal behaviors of the growth rates of action (the rates of holographic complexity) within the "Wheeler-DeWitt"(WDW) patch at the late limit. Furthermore, we find that, for the static neutral cases, when the same mass of black holes is given, the computational speed of the neutral massive black hole is the same as its Einstein gravity counterpart, which is independent with the effect of the graviton mass terms, nevertheless, for the static charged cases, when the same mass and charge parameters of black holes are given, the growth rates of action for the massive charged black holes are always superior to the growth rates of action without graviton mass terms, which directly shows that the massive charged black holes as computers on the computational speeds are faster than their Einstein gravity counterparts.