Prog. Theor. Phys. Vol. 113 No. 4 (2005) pp. 733-761
Self-Force in the Radiation Reaction Formula
— Adiabatic Approximation of a Metric Perturbation and an Orbit
Mail code 130-33, California Institute of Technology, Pasadena, CA 91125, USA
(Received September 20, 2004)
We investigate a calculation method
for the gravitational evolution of an extreme mass ratio binary,
i.e. a binary constituting of a galactic black hole
and a stellar mass compact object.
The inspiralling stage of this system is considered
to be a possible source of detectable gravitational waves.
Because of the extreme mass ratio, one may approximate such a system
by a black hole geometry (a Kerr black hole)
plus a linear metric perturbation induced by a point particle.
With this approximation, a self-force calculation
was proposed for a practical calculation of the orbital evolution,
including the effect of the gravitational radiation reaction,
which is now known as the MiSaTaQuWa self-force.
In addition, a radiation reaction formula was proposed
as an extension of the well-known balance formula of Press and Teukolsky.
The radiation reaction formula provides a convenient method
to calculate an infinite time averaged loss of “the constants of motion"
(i.e. the orbital energy, the z component of the angular momentum,
and the Carter constant) through the gravitational radiation reaction,
with which one may approximately calculate the orbital evolution.
Because these methods are approximately equivalent,
we investigate the consequence of the orbital evolution
using the radiation reaction formula.
To this time, we have used
the so-called adiabatic approximation of the orbital evolution
and considered a method to evaluate the MiSaTaQuWa self-force
by use of a linear metric perturbation. In this approach, we point out that
there is a theoretical question concerning the choice of the gauge condition
in the calculation of the MiSaTaQuWa self-force.
Because of this gauge ambiguity, there is a case in which
the MiSaTaQuWa self-force might not predict the orbital evolution
in a physically expected manner, and this forces us to calculate a waveform
only in the so-called dephasing time.
We discuss the reason that such an unexpected thing happens
and find that it is primarily because we consider
the linear metric perturbation separately
from the orbital evolution due to the self-force.
We propose a new metric perturbation scheme
under a possible constraint of the gauge conditions
in which we obtain a physically expected prediction
of the orbital evolution caused by the MiSaTaQuWa self-force.
In this new scheme of a metric perturbation,
an adiabatic approximation is applied
to both the metric perturbation and the orbit.
As a result, we are able to predict the gravitational evolution of the system
in the so-called radiation reaction time scale,
which is longer than the dephasing time scale.
However, for gravitational wave detection by LISA,
this may still be insufficient.
We further consider a gauge transformation
in this new metric perturbation scheme,
and find a special gauge condition
with which we can calculate the gravitational waveform
of a time scale long enough for gravitational wave detection by LISA.
DOI : 10.1143/PTP.113.733
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Citing Article(s) :
Progress of Theoretical Physics Vol. 115 No. 1 (2006) pp. 43-61
Adiabatic Expansion for a Metric Perturbation and the Condition to Solve the Gauge Problem for the Gravitational Radiation Reaction Problem
Progress of Theoretical Physics Vol. 115 No. 5 (2006) pp. 873-907
Adiabatic Evolution of Orbital Parameters in Kerr Spacetime
Norichika Sago, Takahiro Tanaka, Wataru Hikida, Katsuhiko Ganz and Hiroyuki Nakano
Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145
Gravitational Radiation Reaction