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General Relativity and Quantum Cosmology, gr-qc
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.
