Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations

Abstract

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.

10 pages. Discussion on the role of connections was added. Matches published version

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Cited by in corpus (14)

• Berwald spacetimes and very special relativity
• Reaching the Planck scale with muon lifetime measurements
• Landau Levels in the Presence of a Cosmic String in Rainbow Gravity
• $Ad{S}_4$ dyonic black holes in gravity's rainbow
• Energy Scale of Lorentz Violation in Rainbow Gravity
• Effects of Planck-scale-modified dispersion relations on the thermodynamics of charged black holes
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Lorentz Violation in Finsler Geometry
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• Trajectories of astroparticles in pseudo-Finsler spacetime with the most general modified dispersion
• Revisiting Legendre transformations in Finsler geometry
• Superluminal modes in a quantum field simulator for cosmology from analog trans-Planckian physics