Asymptotic iteration method for spheroidal harmonics of higher-dimensional Kerr-(A)dS black holes

TL;DR

This paper applies the Asymptotic Iteration Method to compute angular eigenvalues of higher-dimensional Kerr-(A)dS black hole spheroidal harmonics, providing new analytic expressions and validating results with the Continued Fraction Method.

Contribution

It introduces the AIM for calculating spheroidal harmonics in higher-dimensional Kerr-(A)dS black holes and derives analytic expressions in the small rotation limit.

Findings

Validated AIM results with CFM

Derived analytic expressions up to O(c^3) and O(α^2)

Provided accurate eigenvalues for higher-dimensional cases

Abstract

In this work we calculate the angular eigenvalues of the $(n+4)$-dimensional {\it simply} rotating Kerr-(A)dS spheroidal harmonics using the Asymptotic Iteration Method (AIM). We make some comparisons between this method and that of the Continued Fraction Method (CFM) and use the latter to check our results. We also present analytic expressions for the small rotation limit up to $O(c^3)$ with the coefficient of each power up to $O(\alpha^2)$, where $c=a\omega$ and $\alpha=a^2 \Lambda$ ($a$ is the angular velocity, $\omega$ the frequency and $\Lambda$ the cosmological constant).