Similarity in the Arnowitt-Deser-Misner Mass from Brill and Teukolsky Initial Data Sets Beyond the Linear Approximation

TL;DR

This paper compares Brill and Teukolsky initial data for vacuum axisymmetric spacetimes, revealing a surprising similarity in their ADM mass distribution related to nonextensive relations, despite structural differences.

Contribution

It demonstrates that Brill and Teukolsky gravitational wave data share a nonextensive relation in ADM mass distribution beyond linear approximation.

Findings

Both data sets satisfy a nonextensive relation.

Structural differences exist at linear and nonlinear levels.

Similarity persists despite distinct multipolar structures.

Abstract

The two most common initial data for vacuum axisymmetric spacetimes are the Brill and Teukolsky gravitational waves. The subsequent numerical evolution of these data exhibits distinct properties mainly associated with the critical gravitational collapse. A possible way of understanding these differences is first to look at the linear level, where the Brill waves have a multipolar structure, while the Teukolsky waves have a quadrupolar structure. Despite being structurally distinct at the linear and nonlinear levels, we show that these gravitational wave initial data share an unexpected similarity related to the distribution of ADM mass as a function of the initial wave's amplitude. More specifically, both configurations satisfy a nonextensive relation, commonly seen in systems governed by long range interactions.