Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons

TL;DR

This paper develops intrinsic Carrollian sigma models using $ ext{R}^ imes$-bundles with connections and applies them to derive a wave equation on a black hole horizon, offering new insights into Carrollian field theories.

Contribution

It introduces a novel intrinsic construction of Carrollian sigma models via $ ext{R}^ imes$-bundles with connections, expanding the understanding of Carrollian field theories.

Findings

Derived a Carrollian wave equation on a Schwarzschild black hole horizon.

Established a new geometric framework for Carrollian sigma models.

Provided a physically motivated example connecting theory to black hole physics.

Abstract

Carrollian field theories are usually understood as limits of relativistic theories. In this note, we use Carrollian $\mathbb{R}^\times$-bundles equipped with a principal connection to construct Carrollian sigma models intrinsically. The resulting theories are neither ``electric'' nor ``magnetic'' in the usual sense. As a physically suggestive example, we derive a Carrollian wave equation governing the dynamics of a scalar field on the event horizon of a Schwarzschild black hole.