Abstract
We study the complexity growth by using complexity = action (CA) proposal in Minimal Massive 3D Gravity(MMG) model which is proposed for resolving the bulk-boundary clash problem of Topologically Massive Gravity(TMG). We observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero.
Highlights
One of the holographic conjectures about the inside of black hole is that its growth is dual to the growth of quantum complexity [1,2]
V we calculate the rate of complexity growth by using the “complexity 1⁄4 action” (CA) conjecture in the minimal massive 3D gravity (MMG) model and we observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero
We consider the topologically massive gravity (TMG) limit of the model and we observe that the rate of the complexity growth saturates the proposed bound by physical mass of the BTZ black hole in the TMG model, when the inner horizon of black hole goes to zero
Summary
One of the holographic conjectures about the inside of black hole is that its growth is dual to the growth of quantum complexity [1,2]. To generalize and make precise Lloyd’s notion of “operations per second,” in [7] authors considered how complexity builds up in an isolated unitary evolving quantum system in a general quantum state They proposed a similar bound on the complexity growth rate based on the works of Aharonov-Anandan-Bohm, Margolus-Levitin and Lloyd [8,9,10,11,12,13].
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