Rotating black hole with a probe string in Horndeski Gravity

TL;DR

This paper investigates how a probe string influences the complexity of a rotating black hole in Horndeski gravity using the CA conjecture, revealing unique complexity behaviors linked to the gravity's parameters.

Contribution

It introduces a novel analysis of black hole complexity in Horndeski gravity with a probe string, employing the Nambu-Goto action to explore time evolution effects.

Findings

Complexity properties are affected by Horndeski gravity parameters.

The probe string's influence on complexity exhibits unique characteristics.

The study provides insights into holographic complexity in modified gravity theories.

Abstract

In this work, we present the effect of a probe string on the complexity of a black hole according to the CA (Complexity equals action) conjecture on Horndeski's gravity. In our system, we consider a particle moving on the boundary of black hole spacetime in ($2+1$)-dimensions. To obtain a dual description, we need to insertion a fundamental string on the bulk spacetime. The effect of this string is given by the Nambu-Goto term. For the Nambu-Goto term, we can analyze the time development of this system, which is affected by the parameters of Horndeski's gravity. In our case, we show some interesting complexity properties for this gravity.