# 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} }

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…

## One Citation

### Black hole based tests of general relativity

- Physics
- 2016

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## 3 References

### A Table of Integrals

- Mathematics
- 2010

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 = −

### New York: Academic Press

- 1965, 4th ed., edited by Geronimus, Yu.V. (4th ed.); Tseytlin, M.Yu. (4th ed.)
- 1965

### and C

- W. Clark, eds., NIST Handbook of Mathematical Functions
- 2010