Evolving testfields in the geometry of a black hole
Andersson, Nils (1997) Evolving testfields in the geometry of a black hole. Physical Review D, 55, (2), 468479. (doi:10.1103/PhysRevD.55.468).
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Description/Abstract
We consider the initial value problem for a massless scalar field in the Schwarzschild geometry. When constructed using a complexfrequency approach the necessary Green’s function splits into three components. We discuss all of these in some detail. (1) The contribution from the singularities (the quasinormal modes of the black hole) is approximated and the mode sum is demonstrated to converge after a certain welldefined time in the evolution. A dynamic description of the mode excitation is introduced and tested. (2) It is shown how a straightforward lowfrequency approximation to the integral along the branch cut in the blackhole Green’s function leads to the anticipated powerlaw falloff at very late times. We also calculate higher order corrections to this tail and show that they provide an important complement to the leading order. (3) The highfrequency problem is also considered. We demonstrate that the combination of the obtained approximations for the quasinormal modes and the powerlaw tail provide a complete description of the evolution at late times. Problems that arise (in the complexfrequency picture) for early times are also discussed, as is the fact that many of the presented results generalize to, for example, Kerr black holes.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1103/PhysRevD.55.468  
Related URLs:  
Subjects:  Q Science > QB Astronomy Q Science > QA Mathematics Q Science > QC Physics 

Divisions :  University Structure  Pre August 2011 > School of Mathematics > Applied Mathematics 

ePrint ID:  29168  
Accepted Date and Publication Date: 


Date Deposited:  07 Feb 2007  
Last Modified:  31 Mar 2016 11:54  
URI:  http://eprints.soton.ac.uk/id/eprint/29168 
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