Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power

TL;DR

This paper investigates gravitational wave emission in quadratic gravity, deriving wave equations, calculating energy and angular momentum radiated, and demonstrating positive energy emission while avoiding instabilities, with an example of a rotating ellipsoid.

Contribution

It provides a detailed analysis of gravitational wave emission in quadratic gravity, including derivation of wave equations and demonstration of positive energy emission avoiding Ostrogradsky instabilities.

Findings

Quadrupole approximation used for analysis

Positive energy and angular momentum emission shown

Massive perturbations affect rotation of a precessing ellipsoid

Abstract

In this paper, the emission of gravitational waves in quadratic gravity theory is examined. The wave equations for massless and massive perturbations are derived, followed by the calculation of the energy and angular momentum radiated. In the quadrupole approximation, and taking into account only the transverse-traceless modes, it is shown that the theory avoids the issues generated by the Ostrogradsky instabilities and achieves positive energy and angular momentum emissions. As an example, a rotating ellipsoid with free precession is analyzed, and the effects of the massive perturbations on its rotation are highlighted.