Cylindrical gravitational waves: radiation and resonance

TL;DR

This paper presents an exact solution for cylindrical gravitational waves, revealing nonlinear effects like monopole radiation and resonance, which differ from the traditional weak field approximation.

Contribution

It provides the first exact solution for cylindrical gravitational waves, highlighting nonlinear phenomena absent in linear approximations.

Findings

Existence of gravitational monopole radiation.

Resonance phenomena in spacetime due to gravitational waves.

Long-term measurements may appear linear despite underlying nonlinear effects.

Abstract

In the weak field approximation the gravitational wave is approximated as a linear wave, which ignores the nonlinear effect. In this paper, we present an exact general solution of the cylindrical gravitational wave. The exact solution of the cylindrical gravitational wave is far different from the weak field approximation. This solution implies the following conclusions. (1) There exist gravitational monopole radiations in the cylindrical gravitational radiation. (2) The gravitational radiation may generate the resonance in the spacetime. (3) The nonlinearity of the gravity source vanishes after time averaging, so the observed result of a long-time measurement may be linear.