How the spherical modes of gravitational waves can be detected despite only seeing one ray

TL;DR

This paper introduces a new gauge in gravitational wave detection that enables extraction of spherical mode information from a single ray by revealing angular derivatives, which are crucial for understanding source properties.

Contribution

The paper presents a novel gauge that makes angular derivatives of gravitational waves visible in detection, allowing for the analysis of spherical modes from a single observation.

Findings

Angular derivatives are of the same order as time derivatives in GW signals.

The new gauge enables constraining spherical modes using a single detection.

The phase evolution of the wave depends on the spherical modes, aiding source characterization.

Abstract

The spherical modes of gravitational waves (GWs) have become a major focus of recent detection campaigns due to the additional information they can provide about different properties of the source. However, GW detection is restricted to only detecting one ray and hence it is not obvious how we can extract information about angular properties. In this paper, we introduce a new gauge that makes visible GW detection does not only contain information on the second time derivative but also on the angular derivatives of the GW. In particular, we show that the angular derivatives are of the same order as the time derivatives of the wave thus allowing us to constrain the spherical modes. To further illustrate the detection of the spherical modes, we discuss how the evolution of the orbit of the source and thus the phase of the wave depends on them.