Gravitational waves from a spinning particle plunging into a Kerr black hole

Abstract

Using a black hole (BH) perturbation approach, we numerically study gravitational waves from a spinning particle of mass $\ensuremath{\mu}$ and spin $s$ on the equatorial plane plunging into a Kerr BH of mass $M$ and spin $a.$ When we take into account the particle spin $s,$ (a) the motion of the particle changes due to the coupling effects between $s$ and the orbital angular momentum ${L}_{z}$ and between $s$ and $a,$ and also (b) the energy momentum tensor of the linearized Einstein equations changes. We calculate the total radiated energy, linear momentum, angular momentum, the energy spectrum, and waveform of gravitational waves, and we find the following features. (1) There are three spin coupling effects: between ${L}_{z}$ and $a,$ between $s$ and ${L}_{z},$ and between $s$ and $a$ when $s$ is considered. Among them, ${(L}_{z}\ensuremath{\cdot}a)$ coupling is the most important effect for the amount of gravitational radiation, and the other two effects are not as remarkable as the first one. However, these effects are still important; for example, the total radiated energy changes by a factor of $\ensuremath{\sim}2$ for the case of $a/M=0.6,$ ${L}_{z}/\ensuremath{\mu}M=1.5$ if we change $s$ from $0$ to $\ensuremath{\lesssim}M.$ (2) For the case when one of the three spins $(a,\phantom{\rule{0ex}{0ex}}{L}_{z},$ and $s)$ is vanishing, the amount of gravitational radiation becomes larger (smaller) if spin axes of the other two are parallel (antiparallel). For the case when three spins are nonvanishing, the amount of gravitational radiation becomes maximum if all the axial directions of $s,$ $a,$ and ${L}_{z}$ coincide. Thus, our calculations indicate that in a coalescence of two black holes (BHs) whose spins and orbital angular momentum are aligned, gravitational waves are emitted most efficiently.