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Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

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arxiv 0903.5319 v1 pith:56JIUJTI submitted 2009-03-31 gr-qc

Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

Marc Casals , Sam Dolan , Adrian Ottewill , Barry Wardell This is my paper
classification gr-qc
keywords functionseriesconvergenceexpansiongreenapproximantsinvestigatepade
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 3 Pith papers

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  3. Early metal-enriched baryon cycling before the midpoint of cosmic reionization

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    The direct Hadamard term for the Teukolsky Green function in Schwarzschild is factored into closed-form S² and exact M² components, enabling regularized ℓ-mode calculations for spin-1 and spin-2 perturbations.