Gravitational radiation of a vibrating physical string as a model for the gravitational emission of an astrophysical plasma

TL;DR

This paper models gravitational wave emission from a vibrating string and extends the approach to astrophysical plasma, introducing novel computational techniques that account for external constraints and relax common assumptions.

Contribution

It develops a new method based on linearized Einstein equations to analyze gravitational radiation from constrained vibrating media, applicable to plasma and astrophysical contexts.

Findings

String vibrations produce gravitational waves independent of frequency.

The method accounts for external constraints affecting emission.

Preliminary numerical results for Alfven waves in the solar corona.

Abstract

The vibrating string is a source of gravitational waves which requires novel computational techniques, based on the explicit construction of a conserved and renormalized (in a classical sense) energy-momentum tensor. The renormalization is necessary to take into account the effect of external constraints, which affect the emission considerably. Vibrating media offer in general a testing ground for reconciling conflicts between General Relativity and other branches of physics; however, constraints are absent in sources like the Weber bar, for which the standard covariant formalism for elastic bodies can also be applied. Our solution method is based on the linearized Einstein equations, but relaxes other usual assumptions like far-field approximation, spherical or plane wave symmetry, TT gauge and source without internal interference. The string solution is then adapted to give the radiation field of a transversal Alfven wave in a rarefied plasma, where the tension is produced by an external static magnetic field. Like for the string, the field strength turns out to be independent from the frequency. We give a preliminary example of a numerical solution based on parameters referred to Alfven waves in the solar corona. Further astrophysical applications require an extension of the solution procedure to second order in the amplitude, and consideration of border effects. Future work will also address numerical and analytical near-field solutions.