A note on the gravitational wave energy spectrum of parabolic and hyperbolic encounters
Matthias Gröbner, Philippe Jetzer, Maria Haney, Shubhanshu Tiwari, Wako Ishibashi
Abstract
Abstract The first calculation of the frequency spectrum of gravitational wave mass quadrupole radiation for binaries on hyperbolic orbits was performed in De Vittori et al (2012 Phys. Rev . D 86 044017). 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.
Topics & Concepts
PhysicsGravitational waveSpectrum (functional analysis)QuadrupoleEnergy (signal processing)Classical mechanicsGravitationFrequency spectrumEnergy spectrumGravitational accelerationHyperbolic functionAstrophysicsRadiationGravitational energyGravitational fieldContinuous spectrumBackground radiationElectromagnetic spectrumGravitational wave backgroundSpectral densityMathematical analysisWave equationTheoretical physicsQuantum electrodynamicsExposition (narrative)Spectral lineGravitational-wave observatoryPulsars and Gravitational Waves ResearchCosmology and Gravitation TheoriesRelativity and Gravitational Theory