Gravitational waves from inspiraling black holes in quadratic gravity

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 $\alpha \lesssim 1.1\times 10^{13}{m}^2$.

19 pages, 9 figures

References in corpus (16)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Observation of gravitational waves from two neutron star-black hole coalescences
• Pulsational Pair-Instability Supernovae
• Planck evidence for a closed Universe and a possible crisis for cosmology
• Black Holes in Higher-Derivative Gravity
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• Where are LIGO's Big Black Holes?
• Massive gravitational waves from the R^2 theory of gravity: production and response of interferometers
• On Gravitational Radiation in Quadratic $f(R)$ Gravity
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• Gravitational waves in higher-order $R^2$ gravity
• Gravitational waves from inspiralling compact binaries in conformal gravity
• Causality constraints in Quadratic Gravity

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• Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints