• Corpus ID: 118082542

Note on Legendre decomposition of the Pontryagin density in Kerr

@article{Stein2014NoteOL,
  title={Note on Legendre decomposition of the Pontryagin density in Kerr},
  author={Leo C. Stein},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2014}
}
  • L. Stein
  • Published 2 July 2014
  • Mathematics
  • arXiv: General Relativity and Quantum Cosmology
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… 
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Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

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