Higher derivative correction to Kaluza-Klein black hole solution

TL;DR

This paper explores how higher derivative corrections influence the attractor mechanism and singularity structure of Kaluza-Klein black holes, demonstrating the existence of attractor solutions and singularity resolution.

Contribution

It provides a detailed analysis of the attractor behavior in Kaluza-Klein black holes with higher derivative terms using effective potential and entropy function formalisms, including $R^n$ corrections.

Findings

Attractor solutions exist with higher derivative corrections.

Higher derivative terms can resolve naked singularities.

Effective potential extremization determines attractor points.

Abstract

We investigate the attractor mechanism in Kaluza-Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as entropy function formalism. We consider different higher derivative terms with a general coupling to moduli field. For the $R^2$ theory, we use effective potential approach, looking for solutions which are analytic near the horizon and show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of $R^n$ terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza-Klein black hole solution we show that higher derivative correction dresses the naked singularity for an appropriate coupling, and we can find the attractor solution.