Energy, Momentum and Angular Momentum of Gravitational Waves Induced by a Particle Plunging into a Schwarzschild Black Hole

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Using the generalized Regge-Wheeler equation, we have computed the energy, the linear momentum and the angular momentum of gravitational waves generated by a particle of mass μ and orbital angular momentum μL_z plunging into a Schwarzschild black hole of mass M(Gtμ). It is found that the maximum value of the radiated linear momentum is 4.5×10^<-2>(μ/M)μc, which suggests the recoil velocity is 120 km/sec for μ=M/10. Although the total energy (ΔE)and the angular momentum (ΔJ) radiated diverge in the limit of L_z→4(GM/c^2)c, the ratio ΔE/ΔJ remains almost constant ~0.15 (c/(GM/c^2)) for L_z ≳(GM /c^2)c. We have also calculated the energy from a ring plunging into a black hole and found that a rotating one always emits less gravitational waves than a non-rotating one. This suggests the collapse of a rotating star may not be always effective for the generation of gravitational radiation.
理論物理学刊行会の論文
1983-09-25