Remarks on DSR and Gravity

TL;DR

This paper compares modifications of special relativity, like DSR and GUP, with classical gravity, revealing conditions for equivalence and effects such as effective repulsion in quantum gravity contexts.

Contribution

It provides a comparative analysis of DSR and GUP modifications with classical gravity, identifying conditions for equivalence and novel effects like repulsion.

Findings

Low energy DSR can be equivalent to Newtonian gravity under restrictive conditions

GUP introduces an effective repulsive effect similar to quantum gravity models

Comparison clarifies the relationship between modified relativity theories and classical gravitational phenomena

Abstract

Modifications of Special Relativity by the introduction of an invariant energy and/or momentum level (so-called Doubly Special Relativity theories, DSR) or by an energy-momentum dependence of the Planck constant (Generalized Uncertainty Principle, GUP) are compared with classical gravitational effects in an interaction processes. For the low energy limit of the usual formulations of DSR to be equivalent with Newtonian gravity, a restrictive condition is found. GUP yields an effective repulsion, in analogy to the gravitational repulsion in loop quantum cosmology.