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# Gravitational Radiations from a Spinning Compact Object around a supermassive Kerr black hole in circular orbit

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### Abstract

The gravitational waves and energy radiations from a spinning compact object with stellar mass in a circular orbit in the equatorial plane of a supermassive Kerr black hole are investigated in this paper. The effect how the spin acts on energy and angular moment fluxes is discussed in detail. The calculation results indicate that the spin of small body should be considered in waveform-template production for the upcoming gravitational wave detections. It is clear that when the direction of spin axes is the same as the orbitally angular momentum ("positive" spin), spin can decrease the energy fluxes which radiate to infinity. For antidirection spin ("negative"), the energy fluxes to infinity can be enlarged. And the relations between fluxes (both infinity and horizon) and spin look like quadratic functions. From frequency shift due to spin, we estimate the wave-phase accumulation during the inspiraling process of the particle. We find that the time of particle inspiral into the black hole is longer for positive spin and shorter for negative compared with the nonspinning particle. Especially, for extreme spin value, the energy radiation near the horizon of the extreme Kerr black hole is much more than that for the nonspinning one. And consequently, the maximum binging energy of the extreme spinning particle is much larger than that of the nonspinning particle.

### Most cited references5

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### Gravitational radiation from a particle in circular orbit around a black hole. II. Numerical results for the nonrotating case

(1993)
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### Electron Spin Resonance inn-Type InSb

(1968)
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### Gravitational waves from a spinning particle in circular orbits around a rotating black hole

(1996)
Using the Teukolsky and Sasaki-Nakamura formalisms for the perterbations around a Kerr black hole, we calculate the energy flux of gravitational waves induced by a {\it spinning} particle of mass $$\mu$$ and spin $$S$$ moving in circular orbits near the equatorial plain of a rotating black hole of mass $$M (\gg \mu)$$ and spin $$Ma$$. The calculations are performed by using the recently developed post-Newtonian expansion technique of the Teukolsky equation. To evaluate the source terms of perturbations caused by a {\it spinning} particle, we used the equations of motion of a spinning particle derived by Papapetrou and the energy momentum tensor of a spinning particle derived by Dixon. We present the post-Newtonian formula of the gravitational wave luminosity up to the order $$(v/c)^5$$ beyond the quadrupole formula including the linear order of particle spin. The results obtained in this paper will be an important guideline to the post-Newtonian calculation of the inspiral of two spinning compact objects.
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### Author and article information

###### Journal
19 August 2010
2010-10-07
1008.3324
10.1103/PhysRevD.82.084013