Statistics – Computation
Scientific paper
Sep 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009gregr..41.2045s&link_type=abstract
General Relativity and Gravitation, Volume 41, Issue 9, pp.2045-2071
Statistics
Computation
2
Hyperbolic Equations, Characteristic Initial Value Problem
Scientific paper
The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.
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