Note on Legendre decomposition of the Pontryagin density in Kerr
Abstract
In arXiv:1406.0957v1 ("Scalar field excited around a rapidly rotating black hole in ChernSimons modified gravity"), Konno and Takahashi have recently developed some analytical results for the scalar field about a Kerr black hole in the decoupling limit of dynamical ChernSimons gravity. This involved a decomposition of the source (the Pontryagin density) in terms of Legendre polynomials. Here we give a twoline expression for this decomposition which simplifies their quadruple sum. Our expressions are rational polynomials multiplying Legendre functions of the second kind, or equivalently rational polynomials multiplying hypergeometric functions.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 DOI:
 10.48550/arXiv.1407.0744
 arXiv:
 arXiv:1407.0744
 Bibcode:
 2014arXiv1407.0744S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 3 pages