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arXiv · 1703.02058

Curved spacetimes with local $\kappa$-Poincar\'e dispersion relation

Leonardo Barcaroli·Lukas K. Brunkhorst·Giulia Gubitosi·Niccoló Loret·Christian Pfeifer
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Abstract

We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $\kappa$-Poincar\'e dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $\kappa$-Poincar\'e dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since photons of different energy will orbit the black hole on circular orbits at different altitudes. We also compute the redshift of a photon between different observers at rest, finding that there is a Planck-scale correction to the usual redshift only if the observers detecting the photon have different masses.

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Leonardo Barcaroli, Lukas K. Brunkhorst, Giulia Gubitosi, Niccoló Loret, Christian Pfeifer. 2017-03-06. Curved spacetimes with local $\kappa$-Poincar\'e dispersion relation. https://doi.org/10.1103/physrevd.96.084010

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