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

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### Abstract

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.

### Most cited references25

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### LIGO: The Laser Interferometer Gravitational-Wave Observatory.

(1992)
The goal of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project is to detect and study astrophysical gravitational waves and use data from them for research in physics and astronomy. LIGO will support studies concerning the nature and nonlinear dynamics of gravity, the structures of black holes, and the equation of state of nuclear matter. It will also measure the masses, birth rates, collisions, and distributions of black holes and neutron stars in the universe and probe the cores of supernovae and the very early universe. The technology for LIGO has been developed during the past 20 years. Construction will begin in 1992, and under the present schedule, LIGO's gravitational-wave searches will begin in 1998.
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### An Approach to Gravitational Radiation by a Method of Spin Coefficients

(1962)
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### Global Structure of the Kerr Family of Gravitational Fields

(1968)
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### Author and article information

###### Journal
19 February 1996
gr-qc/9602038
10.1103/PhysRevD.54.3762
OU-TAP-27
Phys.Rev.D54:3762-3777,1996
20 pages, LaTeX, 2 figures available upon request
gr-qc