Abstract
We consider globally hyperbolic flat spacetimes in 2 + 1 and 3 + 1 dimensions, in which a uniform light signal is emitted on the r-level surface of the cosmological time for r → 0. We show that the frequency shift of this signal, as perceived by a fixed observer, is a well-defined, bounded function which is generally not continuous. This defines a model with anisotropic background radiation that contains information about initial singularity of the spacetime. In dimension 2 + 1, we show that this observed frequency shift 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 frequency shift function for a few simple examples.
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Communicated by James A. Isenberg.
F. Bonsante is partially supported by the A.N.R. through project Geodycos.
C. Meusburger was supported by the DFG Emmy-Noether fellowship ME 3425/1-1.
J.-M. Schlenker was partially supported by the A.N.R. through projects GeomEinstein, ANR-09-BLAN-0116-01 and ETTT, ANR-09-BLAN-0116-01, 2009-13.
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Bonsante, F., Meusburger, C. & Schlenker, JM. Recovering the Geometry of a Flat Spacetime from Background Radiation. Ann. Henri Poincaré 15, 1733–1799 (2014). https://doi.org/10.1007/s00023-013-0300-6
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DOI: https://doi.org/10.1007/s00023-013-0300-6