PIRSA:11030109

Local and Global Properties of Green Functions in Black Hole Space-times

Ottewill, A. (2011). Local and Global Properties of Green Functions in Black Hole Space-times. Perimeter Institute. https://pirsa.org/11030109

Ottewill, Adrian. Local and Global Properties of Green Functions in Black Hole Space-times. Perimeter Institute, Mar. 17, 2011, https://pirsa.org/11030109 

          @misc{ pirsa_PIRSA:11030109,
            doi = {10.48660/11030109},
            url = {https://pirsa.org/11030109},
            author = {Ottewill, Adrian},
            keywords = {Strong Gravity},
            language = {en},
            title = {Local and Global Properties of Green Functions in Black Hole Space-times},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {mar},
            note = {PIRSA:11030109 see, \url{https://pirsa.org}}
          }

Adrian Ottewill

University College Dublin

Talk number
PIRSA:11030109
Collection
Talk Type
Subject
Abstract
The local and global properties of the retarded and Feynman Green functions to the wave equation in curved spacetime are crucial for radiation reaction in the classical theory and for renormalisation in the quantum quantum theory. Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental geometrical bitensors determining the local Hadamard singularity structure of these Green’s functions. We illustrate their use in a semi-recursive approach showing how to determine covariant expansions to high order, for example, calculating the tail term reflecting backscattering by the curvature of spacetime to 20th order in the geodesic separation in a matter of minutes, and as the basis of numerical calculations. We also present an efficient method to construct covariant expansions of the tail term, without using the formal Hadamard light-cone expansion. Finally we discuss the relationship between the geodesic structure, quasi-normal modes with associated excitation factors and the global behaviour of Green functions in black hole space-times.