Comparison of linear Brill and Teukolsky waves

TL;DR

This paper compares linear Brill and Teukolsky gravitational wave initial data to understand their differences and similarities, revealing that under certain conditions, they exhibit surprisingly similar properties despite initial expectations.

Contribution

It provides a detailed comparison of linear Brill and Teukolsky wave data, highlighting conditions under which they behave similarly and explaining differences in their nonlinear evolution.

Findings

Brill waves have higher multipole moments than Teukolsky waves.

For certain seed functions, all higher-order moments vanish in Brill waves.

Linear Brill and Teukolsky data can be surprisingly similar under specific conditions.

Abstract

Motivated by studies of critical phenomena in the gravitational collapse of vacuum gravitational waves we compare, at the linear level, two common approaches to constructing gravitational-wave initial data. Specifically, we construct analytical, linear Brill wave initial data and compare these with Teukolsky waves in an attempt to understand the different numerical behavior observed in dynamical (nonlinear) evolutions of these two different sets of data. In general, the Brill waves indeed feature higher multipole moments than the quadrupolar Teukolsky waves, which might have provided an explanation for the differences observed in the dynamical evolution of the two types of waves. However, we also find that, for a common choice of the Brill-wave seed function, all higher-order moments vanish identically, rendering the (linear) Brill initial data surprisingly similar to the Teukolsky data for a similarly common choice of its seed function.