# Analytic investigation of rotating holographic superconductors

## TL;DR

This paper analytically studies rotating holographic s-wave superconductors in four-dimensional AdS spacetime, examining how black hole rotation influences critical temperature and condensation, and confirming results with multiple analytical methods.

## Contribution

It provides an analytical investigation of rotating holographic superconductors using matching and Sturm-Liouville methods, highlighting the effects of rotation on critical temperature and condensation.

## Key findings

- Rotation affects critical temperature non-trivially
- Analytical results agree with previous numerical findings
- Condensation operators are influenced by black hole rotation

## Abstract

In this paper we have investigated, in the probe limit, $s$-wave holographic superconductors in rotating $AdS_{3+1}$ spacetime using the matching method as well as the St{\"u}rm-Liouville eigenvalue approach. We have calculated the critical temperature using the matching technique in such a setting and our results are in agreement with previously reported results obtained using the St{\"u}rm-Liouville approach. We have then obtained the condensation operators using both analytical methods. The results obtained by both these techniques share the same features as found numerically. We observe that the rotation parameter of the black hole affects the critical temperature and the condensation operator in a non-trivial way.