Journal
PHYSICAL REVIEW D
Volume 96, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.96.084010
Keywords
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Funding
- European Regional Development Fund through Center of Excellence [TK133]
- John Templeton Foundation
- German Research Foundation within Research Training Group 1620 Models of Gravity
- Italian ministry of university and research [000008 15 RS]
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We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the kappa-Poincare 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-Poincare 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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