Apparent Superluminality of Lensed Gravitational Waves

TL;DR

This paper investigates the effects of gravitational lensing on gravitational waves and electromagnetic signals, showing that apparent superluminal GW peaks can occur but do not violate causality, with implications for astrophysics and cosmology.

Contribution

It clarifies the conditions under which gravitational wave signals can appear to arrive before electromagnetic counterparts due to lensing effects.

Findings

GW signals never arrive before EM counterparts if emitted simultaneously.

During binary inspiral, GW peaks can appear before EM signals, but this is only apparent superluminality.

Measuring time delays helps probe lens distribution, gravity, and cosmology.

Abstract

We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. With concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before their EM counterpart. We stress this is only an apparent superluminality since the GW waveform is both distorted and further delayed with respect to light. In any case, measuring the multi-messenger time delay and correctly interpreting it has important implications for unveiling the distribution of lenses, testing the nature of gravity, and probing the cosmological expansion history.