Gravitational radiation from a particle plunging into a Schwarzschild black hole: frequency-domain and semirelativistic analyses

Abstract

We revisit the classic problem of gravitational wave emission by a test particle plunging into a Schwarzschild black hole both in the frequency-domain Regge-Wheeler-Zerilli formalism and in the semirelativistic approximation. We use, and generalize, a transformation due to Nakamura, Sasaki, and Shibata to improve the falloff of the source term of the Zerilli function. The faster decay improves the numerical convergence of quantities of interest, such as the energy radiated at spatial infinity through gravitational waves. As a test of the method, we study the gravitational radiation produced by test particles that plunge into the black hole with impact parameters close to the threshold for scattering. We recover and expand upon previous results that were obtained using the Sasaki-Nakamura equation. In particular, we study the relative contributions to the total energy radiated due to waves of axial and polar parity, and uncover an universal behavior in the waveforms at late times. We complement our study with a semirelativistic analysis of the problem, and we compare the two approaches. The generalized Nakamura-Sasaki-Shibata transformation presented here is a simple and practical alternative for the analysis of gravitational-wave emission by unbound orbits in the Schwarzschild spacetime using the frequency-domain Regge-Wheeler-Zerilli formalism.

arXiv comment16 pages, 10 figures. v2. Matches published version

References in corpus (20)

• Geodesic stability, Lyapunov exponents and quasinormal modes
• "Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole
• Comment on "Kerr Black Holes as Particle Accelerators to Arbitrarily High Energy"
• Approximating the inspiral of test bodies into Kerr black holes
• Semianalytical estimates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters
• Ultra-relativistic grazing collisions of black holes
• Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole
• Gauge Problem in the Gravitational Self-Force I. Harmonic Gauge Approach in the Schwarzschild Background
• Gravitational radiation from infall into a black hole: Regularization of the Teukolsky equation
• Applying the effective-source approach to frequency-domain self-force calculations
• Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge
• Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral
• Comparing numerical and analytical calculations of post-ISCO ringdown amplitudes
• Excitation of Neutron Star Oscillations by an Orbiting Particle
• Scattering of point particles by black holes: gravitational radiation
• Unbound motion on a Schwarzschild background: Practical approaches to frequency domain computations
• Stellar Pulsations excited by a scattered mass
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Multipolar gravitational waveforms and ringdowns generated during the plunge from the innermost stable circular orbit into a Schwarzschild black hole
• Regularization of the Teukolsky Equation for Rotating Black Holes

Cited by in corpus (4)

• Quasinormal modes and their excitation beyond general relativity
• Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole
• Gravitational memory: new results from post-Newtonian and self-force theory
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results