Abstract
Based on the context of complexity = action (CA) conjecture, we calculate the holographic complexity of AdS black holes with planar and spherical topologies in Horndeski theory. We find that the rate of change of holographic complexity for neutral AdS black holes saturates the Lloyd’s bound. For charged black holes, we find that there exists only one horizon and thus the corresponding holographic complexity can’t be expressed as the difference of some thermodynamical potential between two horizons as that of Reissner–Nordstrom AdS black hole in Einstein–Maxwell theory. However, the Lloyd’s bound is not violated for charged AdS black hole in Horndeski theory.
Highlights
Where F is the free energy, T, S are the temperature and entropy of the black hole, and H = F +T S is the generalized enthalpy
Horndeski theory is a kind of higher derivative scalartensor theory which has the similar property of Lovelock gravity, that the Largrangian involves terms which are more than two derivatives, but the equations of motion are consisted of terms which have at most two derivatives acting on each field [37]
Holographic application of Horndeski theory were investigated in [45,46,47,48,49,50,51,52], especially, it was shown in [51] that there is no holographic a-theorem for general Horndeski gravity, there does exist a critical point in parameter space where the holographic a-theorem can be achieved, which suggests the Horndeski theory should have a holographic field theory dual
Summary
It was pointed out that the action growth expression is different for charged black hole with a single horizon in the Einstein–Maxwell–Dilaton and Born–Infeld theories [36]. It is worthwhile taking a further step to explore the pattern of the action growth of charged AdS black holes with only one horizon in higher derivative gravity theory. We shall study the action growth of AdS black holes in Horndeski gravity theory. The AdS black holes we studied in this paper are in this critical point.
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