Kavli Affiliate: Xian Chen
| First 5 Authors: Han Yan, Xian Chen, Alejandro Torres-Orjuela, ,
| Summary:
The possibility of forming gravitational-wave sources with high
center-of-mass (c.m.) velocities in the vicinity of supermassive black holes
requires us to develop a method of deriving the waveform in the observer’s
frame. Here we show that in the limit where the c.m. velocity is high but the
relative velocities of the components of the source are small, we can solve the
problem by directly integrating the relaxed Einstein field equation. In
particular, we expand the result into multipole components which can be
conveniently calculated given the orbit of the source in the observer’s frame.
Our numerical calculations using arbitrary c.m. velocities show that the result
is consistent with the Lorentz transformation of GWs to the leading order of
the radiation field. Moreover, we show an example of using this method to
calculate the waveform of a scattering event between the high-speed ($sim
0.1c$) stellar objects embedded in the accretion disk of an active galactic
nucleus. Our multipole-expansion method not only has advantages in analyzing
the results from stellar-dynamical models but also provides new insight into
the multipole properties of the GWs emitted from a high-speed source.
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