Francesco Bonsante, Catherine Meusburger, Jean-Marc Schlenker
We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, where a uniform light signal is emitted on the $r$-level surface of the cosmological time for $r\to 0$. We show that the intensity of this signal, as perceived by a fixed observer, is a well-defined, bounded function which is generally not continuous. This defines a purely classical model with anisotropic background radiation that contains information about initial singularity of the spacetime. In dimension 2+1, we show that this observed intensity function is stable under suitable perturbations of the spacetime, and that, under certain conditions, it contains sufficient information to recover its geometry and topology. We compute an approximation of this intensity function in a few simple examples.
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http://arxiv.org/abs/1302.6966
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