Metric Perturbations Induced by a Particle Falling into a Schwarzschild Black Hole. I : Formulation : Astrophysics and Relativity

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Metric perturbations induced by a test particle and a spheroidal dust shell falling straightly into a Schwarzschild black hole are examined in radial as well as isothermal gauge conditions. We calculate the wave forms at several radii. We find that the wave form of the quasi-normal mode is essentially the same, but the wave form of the precursor depends on the radius. For one particle case, the metric perturbation does not approach zero for ∣t∣→∞ and it also depends on the gauge conditions, while for a spheroidal dust shell case, it approaches zero for ∣t∣→∞ irrespective of gauges. As for the energy flux in the radial gauge, we find that to estimate the energy flux within 20 percent accuracy we need r〜40 M for the dust shell case, while for one particle case we need at least r〜150 M. This suggests that in two body problem such as the collision of two black holes or coalescing binary neutron stars in numerical relativity, we must carefully treat the metric to estimate the energy flux.
理論物理学刊行会の論文
1992-05-25