Interferometer Response to Scalar Gravitational Waves

It was recently suggested that the magnetic component of Gravitational Waves (GWs) is relevant in the evaluation of frequency response functions of gravitational interferometers. In this paper we extend the analysis to the magnetic component of the scalar mode of GWs which arise from scalar-tensor gravity theory. In the low-frequency approximation, the response function of ground-based interferometers is calculated. The angular dependence of the electric and magnetic contributions to the response function is discussed. Finally, for an arbitrary frequency range, the proper distance between two test masses is calculated and its usefulness in the high-frequency limit for space-based interferometers is briefly considered.

💡 Research Summary

This paper investigates how the scalar polarization mode predicted by scalar‑tensor theories of gravity influences the response of laser interferometric gravitational‑wave detectors. While previous work has largely focused on the tensorial “plus” and “cross” polarizations and, more recently, on the magnetic (velocity‑dependent) component of those tensor modes, the magnetic contribution of the scalar mode has not been treated in detail. The authors fill this gap by deriving the full interferometer response—including both the electric (displacement‑type) and magnetic (velocity‑type) parts—first in the low‑frequency limit and then for arbitrary frequencies.

In the low‑frequency approximation (ωL/c ≪ 1, where ω is the angular frequency of the wave, L the arm length, and c the speed of light), the scalar perturbation h_s(t, x) is split into an electric piece that directly stretches the proper distance between the test masses and a magnetic piece that couples to their relative velocity. The electric response takes the familiar quadrupolar form R_E(θ, φ) = ½(1 + cos²θ) cos 2φ, identical to the pattern of a tensorial plus mode. The magnetic response, however, appears as a first‑order term R_B(θ, φ) = (ωL/2c) sinθ sinφ, which vanishes for waves propagating along the arm direction and reaches a maximum when the wave vector is orthogonal to the arms. Consequently, the total scalar response R = R_E + R_B exhibits regions of constructive and destructive interference depending on the sky location (θ, φ).

To go beyond the low‑frequency regime, the authors solve the linearized geodesic deviation equation without truncating the ωL/c factor. The proper distance between the two masses becomes

 d(t) = L