General spherical harmonic bra-ket overlap integrals of trigonometric functions. (2nd March 2023)

• Record Type: Journal Article
• Authors: Lingetti, Giuseppe; Pani, Paolo
• Is Part Of: Classical and quantum gravity. Volume 40:Number 5(2023)
• Publication Date: 2023-03-02
• Subjects: spherical harmonics -- overlap -- integrals -- mathematical physics -- spherical harmonic decomposition -- wave equations -- perturbation theory; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/acb880
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: Closed formulas in terms of double sums of Clebsch–Gordan coefficients are computed for the evaluation of bra-ket spherical harmonic overlap integrals of a wide class of trigonometric functions. These analytical expressions can find useful application in problems involving non-separable wave equations, e.g. general-relativistic perturbation theory, electromagnetism, quantum theory, etc, wherein the overlap integrals arise from the coupling among different angular modes. We provide some examples related to linear perturbations of spinning black holes in general relativity and modified gravity, in which the analytical formulas for the overlap integrals are particularly useful to compute the black-hole spectrum.