Padé approximants of the Green function in spherically symmetric spacetimes

Marc Casals, Sam Dolan, Adrian C. Ottewill, and Barry Wardell
Phys. Rev. D 79, 124044 – Published 29 June 2009

Abstract

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 Padé 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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  • Received 20 April 2009

DOI:https://doi.org/10.1103/PhysRevD.79.124044

©2009 American Physical Society

Authors & Affiliations

Marc Casals*

  • CENTRA, Instituto Superior Técnico, Lisbon, Portugal and School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland

Sam Dolan, Adrian C. Ottewill, and Barry Wardell§

  • Complex and Adaptive Systems Laboratory and School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

  • *marc.casals@dcu.ie
  • sam.dolan@ucd.ie
  • adrian.ottewill@ucd.ie
  • §barry.wardell@ucd.ie

See Also

Self-force calculations with matched expansions and quasinormal mode sums

Marc Casals, Sam Dolan, Adrian C. Ottewill, and Barry Wardell
Phys. Rev. D 79, 124043 (2009)

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Vol. 79, Iss. 12 — 15 June 2009

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