11,347 research outputs found
Integral formulation of the measured equation of invariance
A novel integral formulation of the measured equation of invariance is derived from the reciprocity theorem. This formulation leads to a sparse matrix equation for the induced surface current, resulting in great CPU time and memory savings over the conventional approaches. The algorithm has been implemented for two-dimensional perfectly conducting scatterers.Peer ReviewedPostprint (published version
On the Global Hadamard form for the Green Function in Schwarzschild space-time
The retarded Green function of a wave equation on a 4-dimensional curved
background space-time is a (generalized) function of two space-time points and
diverges when these are connected by a null geodesic. The Hadamard form makes
explicit the form of this divergence but only when one of the points is in a
normal neighbourhood of the other point. In this paper we derive a global in
time representation for the retarded Green function for a scalar field in
Schwarzschild space-time which makes explicit its complete singularity
structure. We interpret this representation as a sum of Hadamard forms, the
summation being taken over the number of times the null wavefront has passed
through a caustic point. Our representation is valid everywhere except in a
neighbourhood of caustic points. We deal with these points by providing a
separate representation for the Green function which makes explicit its
(different) singularity structure specifically at caustics.Comment: 29 pages, 3 figures. In version 3 we include numerical evidence for
our analytical results as well as small corrections with respect to the
previous versio
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