Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

Details Pade Approximants of the Green Function in Spherically Symmetric Spacetimes Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

2009-03-31

arxiv.org/abs/0903.5319v1

Phys.Rev.D79:124044,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 12 figures

Scientific paper

10.1103/PhysRevD.79.124044

We investigate the scalar Green function for spherically symmetric spacetimes expressed as a coordinate series expansion in the separation of the points. We calculate the series expansion of the function $V(x,x')$ appearing in the Hadamard parametrix of the scalar Green function to very high order. This expansion is then used to investigate the convergence properties of the series and to estimate its radius of convergence. Using the method of Pade approximants, we show that the series can be extended beyond its radius of convergence to within a short distance of the normal neighborhood boundary.

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