Complexity growth of rotating black holes with a probe string

TL;DR

This paper investigates how a probe string affects the growth of complexity in rotating black holes within the CA conjecture framework, providing insights into complexity in quantum field theories.

Contribution

It introduces the effect of a probe string via the Nambu-Goto action on black hole complexity, offering new understanding of complexity dynamics in holographic systems.

Findings

Probe string influences complexity growth patterns.

Analysis reveals properties of complexity related to string dynamics.

Provides insights into defining complexity in quantum field theories.

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.