Observables from spherically symmetric modified dispersion relations

TL;DR

This paper investigates how modified dispersion relations, including quantum gravity-inspired and medium-induced types, affect observable phenomena like black hole shadows and light deflection in spherical symmetry, providing potential experimental tests.

Contribution

It systematically derives corrections to key gravitational observables from general and -Poincare9 dispersion relations in spherical symmetry, highlighting measurable effects.

Findings

Corrections to photon sphere and black hole shadow derived

Modified dispersion relations introduce observable dependencies on photon momentum

Results applicable to quantum gravity phenomenology and plasma physics

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 $\kappa$-Poincar\'e dispersion relation in spherical symmetry. We derive the corrections to the photon sphere, the black hole shadow, 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.