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 Chern-Simons 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 Chern-Simons gravity. This involved a decomposition of the source (the Pontryagin density) in terms of Legendre polynomials. Here we give a two-line 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:
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arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.0744
- arXiv:
- arXiv:1407.0744
- Bibcode:
- 2014arXiv1407.0744S
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 3 pages