New instability in relativistic cylindrically symmetric system

TL;DR

This paper reveals an instability in a relativistic cylindrical shell of counter-rotating dust, showing it cannot settle into static equilibrium due to gravitational radiation, unlike in Newtonian gravity.

Contribution

It demonstrates that certain initial conditions lead to persistent gravitational radiation emission, preventing the system from reaching a static state in general relativity.

Findings

Some initial data do not settle into equilibrium.

Infinite gravitational radiation is emitted to null infinity.

The system exhibits a relativistic instability not present in Newtonian gravity.

Abstract

We investigate an infinitesimally thin cylindrical shell composed of counter-rotating dust particles. This system was studied by Apostolatos and Thorne in terms of the C-energy for a bounded domain. In this paper, we reanalyze this system by evaluating the C-energy on the future null infinity. We find that some class of momentarily static and radiation-free initial data does not settle down into static, equilibrium configurations, and otherwise infinite amount of the gravitational radiation is emitted to the future null infinity. Our result implies the existence of an instability in this system. In the framework of the Newtonian gravity, a cylindrical shell composed of counter-rotating dust particles can be in a steady state with oscillation by the gravitational attraction and centrifugal repulsion, and hence a static state is not necessarily realized as a final state. By contrast, in the framework of general relativity, the steady oscillating state will be impossible since the gravitational radiation will carry the energy of the oscillation to infinity. Thus, this instability has no counterpart in the Newtonian gravity.