Revisiting the Carrollian Scalar Field

TL;DR

This paper explores the dynamics and conservation laws of conformally coupled scalar fields in Carrollian spacetimes, revealing electric and magnetic behaviors and their relation to conformal symmetries, with applications to Ricci-flat spacetimes.

Contribution

It provides a comprehensive analysis of scalar field dynamics, energy, and momentum in Carrollian geometries, including conservation laws and applications to specific spacetime boundaries.

Findings

Discovered electric and magnetic dynamics of scalar fields in Carrollian spacetime

Derived energy and momentum expressions with conservation equations

Applied results to scalar fields on null boundaries of Ricci-flat spacetimes

Abstract

We investigate the (conformally coupled) scalar field on a general Carrollian spacetime in arbitrary dimension. The analysis discloses electric and magnetic dynamics. For both, we provide the energy and the momenta of the field, accompanied by their conservation equations. We discuss the conservation and non-conservation properties resulting from the existence of conformal isometries and the associated charges. We illustrate those results for a scalar field propagating on the null boundary of four-dimensional Ricci-flat Robinson--Trautman spacetimes.