Observables from spherically symmetric modified dispersion relations

Abstract

In this work we continue the systematic study of observable effects emerging from modified dispersion relations. We study the motion of test particles subject to a general first order modification of the general relativistic dispersion relation as well as subject to the κ-Poincaré dispersion relation in spherical symmetry. We derive the corrections to the photon sphere, the Shapiro delay and the light deflection and identify the additional dependence of these observables on the photons' four momentum, which leads to measurable effects that can be compared to experimental data. The results presented here can be interpreted in two ways, depending on the origin of the modified dispersion relation: on the one hand as prediction for traces of quantum gravity, when the modified dispersion relation is induced by phenomenological approaches to quantum gravity, on the other hand as predictions of observables due to the presence of a medium, like a plasma, which modifies the dispersion relation of light on curved spacetimes.

Particles in Loop Quantum Gravity formalism: a thermodynamical description

“…The possibility of Planck-scale modifications of the dispersion relation has been extensively considered in the quantum gravity literature [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and, specifically, in Loop Quantum Gravity scenario [46][47][48][49][50][51][52][53]. Although customarily many examinations begin theirs investigations with the action associated with a particular theory, there exists a prominent alternative manner in the literature of addressing physical results from its dispersion relation only [29].…”