Relative Locality in Curved Space-time

TL;DR

This paper develops a framework for describing particle dynamics in curved spacetime with non-trivial momentum space geometry, extending previous flat or maximally symmetric cases to more general geometries, with potential implications for quantum gravity phenomenology.

Contribution

It introduces a new action formulation for particles in curved spacetime with curved momentum space, exemplified by the kappa-Poincaré case in Schwarzschild spacetime.

Findings

Momentum space curvature effects are negligible in the Schwarzschild example.

The framework generalizes previous models to arbitrary spacetime geometries.

Analysis relies on solving the soccer ball problem.

Abstract

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.