Gravitational waves from inspiraling black holes in quadratic gravity

TL;DR

This paper investigates gravitational waves from inspiraling black holes within quadratic gravity, identifying additional massive modes, analyzing their effects, and proposing constraints on the theory's parameters based on waveforms and coalescence time data.

Contribution

It provides a linearized analysis of gravitational waves in quadratic gravity, identifies the presence of massive modes, discusses their physical implications, and introduces methods to constrain the theory's parameters.

Findings

Identification of massive spin-2 and spin-0 modes in quadratic gravity.

Constraints on the parameter alpha from waveform and coalescence time analysis.

Abstract

We peform a study of gravitational waves emitted by inspiraling black holes in the context of quadratic gravity. By linearizing the field equations around a flat background, we demonstrate that all degrees of freedom satisfy wave-like equations. These degrees of freedom split into three modes: a massive spin-$2$ mode, a massive spin-$0$ mode, and the expected massless spin-$2$ mode. We construct the energy-momentum tensor of gravitational waves and show that, due to the massive spin-$2$ mode, it presents the Ostrogradski instability. We also show how to deal with this possible pathology and obtain consistent physical interpretations for the system. Using the energy-momentum tensor, we study the influence of each massive mode in the orbital dynamics and compare it with the standard result of General Relativity. Moreover, we present two methods to constrain the parameter $\alpha$ associated with the massive spin-$2$ contribution. From the first method, using the combined waveform for the spin-$2$ modes, we obtain the constraint $ \alpha \lesssim 1.1 \times 10^{21} m^{2}$. In the second method, using the coalescence time, we get the constraint $ \alpha \lesssim 1.1 \times 10^{13} m^{2}$.