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

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

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983pthph..70..757o&link_type=abstract

Progress of Theoretical Physics, Vol. 70, No. 3, pp. 757-771

Physics

24

Scientific paper

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 μ Lz plunging into a Schwarzschild black hole of mass M(>> μ). It is found that the maximum value of the radiated linear momentum is 4.5 × 10-2(μ/ M)μ c, which suggests the recoil velocity is 120 km/ sec for μ=M/ 10. Although the total energy (Δ E) and the angular momentum (Δ J) radiated diverge in the limit of Lz → 4(GM/ c2)c, the ratio Δ E/ Δ J remains almost constant ˜ 0.15 (c/ (GM/ c2)) for Lz >˜ (GM/ c2)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 rediation.

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