Gravitational Waves from a Particle Scattered by a Schwarzschild Black Hole : Astrophysics and Relativity

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Using the generalized Regge-Wheeler equation, we have computed the gravitational radiation emitted by a particle of mass μ with orbital angular momentum μL_z(L_z>4(GM/c^2)c) and the total energy μc^2 scattered by a Schwarzschild black hole of mass M(≫μ). It is found that contrary to plunging cases (L_z<4(GM/c^2)c), the quasi-normal mode is not excited even when the periastron approaches the limiting value 4(GM/c^2). The total energy for L_z=4.1(GM/c^2)c is 1.24×10^<-1>(μ/M)μc^2 which is smaller than that for L_z=3.9(GM/c^2)c, 5.49×10^<-1>(μ/M)μc^2. The peak of the energy spectrum is not determined by the quasi-normal mode but by the angular velocity of the particle at the periastron. We have also calculated the energy from a rotating ring scattered by the black hole. In this case, the energy does not diverge in the limit L_z →4(GM/c^2)c. However, it has discontinuity at L_z=4(GM/c^2)c, which is due to the frigidity of a black hole to a scattered particle.
理論物理学刊行会の論文
1984-01-25