Abstract
In this paper, we investigate the holographic complexity in the charged Taub-NUT-AdS black holes with Misner strings present in the Einstein-Maxwell gravity. We show that differing from the normal black holes, where the late-time complexity growth rate is only determined by the quantities at outer and inner ``Reissner-Nordstrom''-type (RN-type) horizons, here the quantities (the Misner potential and Misner charge) related to the Misner strings also play an important role in CA complexity. Similar to the case of the normal electromagnetic black hole, the late-time rate for the original CA conjecture is independent on the magnetic charges. However, disparate with common results of the dyonic solutions, the electric charge appeared here is the total charge of this black hole. Besides, we found that the result in this original CA conjecture also violates the electromagnetic duality. And this duality can be restored by adding the Maxwell boundary term with the proportional constant $\g=1/2$. In this case, the late-time rate is sensitive to the magnetic charge. Moreover, we also found that the additional term only changes the proportion between the electric and magnetic charges, and it does not affect the Misner term appeared in the late-time rate. Finally, we studied the time-dependence of the complexity growth rate and found that they share similar behaviors with that in RN-AdS black holes.
Highlights
In recent years, there has been a growing interest in the topic of “quantum complexity,” which is defined as the minimum number of gates required to obtain a target state starting from a reference state [1,2]
One can verify that this result violates the electromagnetic duality of the Maxwell theory. It was recently proposed in Ref. [51] that this electromagnetic duality can be restored by adding the Maxwell boundary terms
We investigated the holographic complexity in the charged Taub-NUT-anti–de Sitter (AdS) black holes with two RN-type horizons present in the Einstein-Maxwell gravity
Summary
There has been a growing interest in the topic of “quantum complexity,” which is defined as the minimum number of gates required to obtain a target state starting from a reference state [1,2]. As one of the most interesting solutions of general relativity, Taub-NUT spacetime [68,69] has engendered lots of investigations since birth In this spacetime, apart from the Reissner-Nordstrom (RN)-type horizons, there exist two Misner string singularities on the north and south pole axes due to the existence of Newman-UntiTamburino (NUT) parameter n. Apart from the Reissner-Nordstrom (RN)-type horizons, there exist two Misner string singularities on the north and south pole axes due to the existence of Newman-UntiTamburino (NUT) parameter n This Misner string is a Killing horizon of this black hole, and it will change the topology of the spacetime geometry, especially the late-time boundaries of the WDW patch.
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