Geodesics in Carrollian Reissner-Nordstr\"om black holes

TL;DR

This paper investigates the structure of geodesics in Carrollian Reissner-Nordström black holes, revealing how ultra-relativistic limits alter spacetime patches and particle trajectories, with distinctions between neutral and charged particles.

Contribution

It provides a detailed analysis of geodesic structures in Carrollian RN black holes, including the effects of ultra-relativistic limits and electromagnetic interactions on particle trajectories.

Findings

Geodesics are well-defined in Carrollian RN spacetimes.

Ultra-relativistic limits squeeze the global structure of RN black holes.

Charged particles exhibit significantly different trajectories from neutral ones.

Abstract

In this work, we study the geodesics in different types of Carrollian RN (Reissner-Nordstr\"om) black holes, considering the motions of both neutral and charged particles. We use the geodesic equations in the weak Carrollian structure and analyze the corresponding trajectories projected onto the absolute space, and find that the geodesics are well-defined. In particular, we examine the electric-electric and magnetic-electric limit of the RN black hole, focusing on their geodesic structures. We find that the global structures of the usual RN black holes get squeezed under the ultra-relativistic limit. More precisely, the nonextreme magnetic-electric RN spacetime has two different asymptotic flat patches while the extreme black hole spacetime consists of only one patch. For the magnetic-electric RN spacetime, the Carrollian extremal surfaces (CESs) divide the spacetime into several geodesically complete regions, and the geodesics can only travel in one of these regions. For the charged particles, we extend the analysis by considering their interactions with the electromagnetic field in the Carrollian RN spacetimes and find that their trajectories are significantly different from the neutral geodesics.