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Advances in High Energy Physics
Volume 2017 (2017), Article ID 6075920, 8 pages
Research Article

Planck-Scale Dual-Curvature Lensing and Spacetime Noncommutativity

1Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma, Italy
2Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, Golm, 14476 Potsdam, Germany

Correspondence should be addressed to Giovanni Amelino-Camelia

Received 10 May 2017; Accepted 22 June 2017; Published 10 August 2017

Academic Editor: Sally Seidel

Copyright © 2017 Giovanni Amelino-Camelia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


It was recently realized that Planck-scale momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual-curvature lensing, a feature which mainly affects the direction of observation of particles emitted by very distant sources. Several gray areas remain in our understanding of dual-curvature lensing, including the possibility that it might be just a coordinate artifact and the possibility that it might be in some sense a by-product of the better studied dual-curvature redshift. We stress that data reported by the IceCube neutrino telescope should motivate a more vigorous effort of investigation of dual-curvature lensing, and we observe that studies of the recently proposed “-Minkowski noncommutative spacetime” could be valuable from this perspective. Through a dedicated -Minkowski analysis, we show that dual-curvature lensing is not merely a coordinate artifact and that it can be present even in theories without dual-curvature redshift.