Abstract
We study the effect of a probe string to black hole complexity according to the CA (Complexity equals Action) conjecture. Our system contains a particle moving on the boundary of black hole spacetime. In the dual description this corresponds to the insertion of a fundamental string on the bulk spacetime. The total action consists of the Einstein-Hilbert term and the Nambu-Goto term. The effect of this string is expressed by the Nambu-Goto term. Focusing on the Nambu-Goto term, we analyse the time development of this system. Our results show some interesting properties of complexity. This gives a useful hint for defining complexity in quantum field theories.
Highlights
The concept of computational complexity was originally known in quantum information theory [1,2,3,4,5,6,7] or computer science [8,9]
Complexity is realized as an important quantity for studying the structure of black hole spacetime—the Einstein-Rosen bridge [23,24,25,26,27,28,29,30,31], which is a structure of connecting two external black holes thought to be equivalent to an entangled pair of particles (ER 1⁄4 EPR) [32]
On the other hand we study the effect of the probe string here
Summary
The concept of computational complexity was originally known in quantum information theory [1,2,3,4,5,6,7] or computer science [8,9]. In a previous paper [126] we studied the effect of the probe string moving on the AdS3þ1 black hole spacetime. In this paper we try to find new properties of complexity by studying the effects of the probe string on a more broad type of black hole. II we begin with calculating the effect of the probe string on the AdS black hole This is a higher-dimensional generalization of the previous work. Their complexity growth is studied in Ref. The drag force of the four-dimensional Kerr-AdS black hole is studied in Ref. Action—The NG action is obtained by integrating over the WDW patch:
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