# Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects

## TL;DR

This paper investigates the energy content and dynamical effects of cylindrical gravitational waves using C-energy and super-energy concepts, analyzing particle interactions and spacetime strains caused by such waves.

## Contribution

It introduces a detailed analysis of gravitational wave energy using local energy descriptions and explores particle dynamics and spacetime strains beyond simple geodesic motion.

## Key findings

- Particles experience a Poynting-Robertson-like effect due to wave interaction.
- Spacetime strains reveal invariant curvature effects from gravitational waves.
- Explicit examples include monochromatic and pulsed gravitational waves.

## Abstract

The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel-Robinson super-energy tensor. A Poynting-Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displaced orthogonally to the direction of propagation of the wave are examined, providing invariant information on spacetime curvature effects caused by the passage of the wave. The explicit examples of monochromatic waves with either a single or two polarization states as well as pulses of gravitational radiation are discussed.