A note on the gravitational wave energy spectrum of parabolic and hyperbolic encounters

Abstract

The first calculation of the frequency spectrum of gravitational wave mass quadrupole radiation for binaries on hyperbolic orbits was performed in arXiv:1207.5359. Some shortcomings of their derivation were pointed out, but there are still inaccuracies and supplements that we believe are worthwhile to communicate. In this note we provide a consistent and straightforward exposition of the frequency spectrum in the case of hyperbolic encounters and explicitly determine the parabolic limit, which was not possible with the previous treatments.

References in corpus (6)

• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• Detection Rate Estimates of Gravity-waves Emitted During Parabolic Encounters of Stellar Black Holes in Globular Clusters
• Gravitational wave energy spectrum of hyperbolic encounters
• Gravitational wave bursts from Primordial Black Hole hyperbolic encounters
• Gravitational waves from spinning compact binaries in hyperbolic orbits
• Gravitational wave energy spectrum of a parabolic encounter

Cited by in corpus (14)

• The Science of the Einstein Telescope
• The stochastic gravitational wave background from close hyperbolic encounters of primordial black holes in dense clusters
• Challenges and Opportunities of Gravitational Wave Searches above 10 kHz
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Frequency space derivation of linear and non-linear memory gravitational wave signals from eccentric binary orbits
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Effects of orbital precession on hyperbolic encounters
• Detectability of stochastic gravitational wave background from weakly hyperbolic encounters
• Gravitational bremsstrahlung in plasmas and clusters
• Mass octupole and current quadrupole corrections to gravitational wave emission from close hyperbolic encounters
• Gravitational wave background from primordial black holes in globular clusters
• Interactions among binary black holes in star clusters: Eccentric gravitational wave captures and triple formation
• Frequency domain analysis of the gravitational wave energy loss in hyperbolic encounters
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order