Complexity growth for topological black holes by holographic method

TL;DR

This paper investigates how the complexity growth, measured by action, varies for topological black holes with different horizon curvatures using holographic methods, highlighting unique behavior for toroidal horizons.

Contribution

It compares the action growth of black holes with positive, negative, and zero curvature horizons, revealing distinct behavior for toroidal black holes within the complexity-action framework.

Findings

Toroidal black holes show unique action growth behavior.

Black holes with different topologies exhibit distinct complexity dynamics.

Probe strings behave differently depending on horizon topology.

Abstract

We consider the growth of the action for black hole spacetime with a fundamental string. Our interest is to find the difference of the behavior between black holes with three different topologies in the scenario of complexity-action conjecture. These black holes have positive, negative and zero curvatures. We would like to calculate the action growth of these systems with a probe fundamental string according to the complexity-action conjecture. We find that for the case where the black holes have the toroidal horizon structure this probe string behaves very differently from the other two cases.