25 research outputs found
An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
We develop a numerical code to compute gravitational waves induced by a
particle moving on eccentric inclined orbits around a Kerr black hole. For such
systems, the black hole perturbation method is applicable. The gravitational
waves can be evaluated by solving the Teukolsky equation with a point like
source term, which is computed from the stress-energy tensor of a test particle
moving on generic bound geodesic orbits. In our previous papers, we computed
the homogeneous solutions of the Teukolsky equation using a formalism developed
by Mano, Suzuki and Takasugi and showed that we could compute gravitational
waves efficiently and very accurately in the case of circular orbits on the
equatorial plane. Here, we apply this method to eccentric inclined orbits. The
geodesics around a Kerr black hole have three constants of motion: energy,
angular momentum and the Carter constant. We compute the rates of change of the
Carter constant as well as those of energy and angular momentum. This is the
first time that the rate of change of the Carter constant has been evaluated
accurately. We also treat the case of highly eccentric orbits with . To
confirm the accuracy of our codes, several tests are performed. We find that
the accuracy is only limited by the truncation of -, - and -modes,
where is the index of the spin-weighted spheroidal harmonics, and
and are the harmonics of the radial and polar motion, respectively. When we
set the maximum of to 20, we obtain a relative accuracy of
even in the highly eccentric case of . The accuracy is better for lower
eccentricity. Our numerical code is expected to be useful for computing
templates of the extreme mass ratio inspirals, which is one of the main targets
of the Laser Interferometer Space Antenna (LISA).Comment: Reference added in section
A new analytical method for self-force regularization II. Testing the efficiency for circular orbits
In a previous paper, based on the black hole perturbation approach, we
formulated a new analytical method for regularizing the self-force acting on a
particle of small mass orbiting a Schwarzschild black hole of mass ,
where . In our method, we divide the self-force into the -part and -part. All the singular behaviors are contained in the
-part, and hence the -part is guaranteed to be regular. In
this paper, focusing on the case of a scalar-charged particle for simplicity,
we investigate the precision of both the regularized -part and the
-part required for the construction of sufficiently accurate
waveforms for almost circular inspiral orbits. For the regularized -part, we calculate it for circular orbits to 18 post-Newtonian (PN) order
and investigate the convergence of the post-Newtonian expansion. We also study
the convergence of the remaining -part in the spherical harmonic
expansion. We find that a sufficiently accurate Green function can be obtained
by keeping the terms up to .Comment: 21pages, 12 figure
Self-force Regularization in the Schwarzschild Spacetime
We discuss the gravitational self-force on a particle in a black hole
space-time. For a point particle, the full (bare) self-force diverges. The
metric perturbation induced by a particle can be divided into two parts, the
direct part (or the S part) and the tail part (or the R part), in the harmonic
gauge, and the regularized self-force is derived from the R part which is
regular and satisfies the source-free perturbed Einstein equations. But this
formulation is abstract, so when we apply to black hole-particle systems, there
are many problems to be overcome in order to derive a concrete self-force.
These problems are roughly divided into two parts. They are the problem of
regularizing the divergent self-force, i.e., ``subtraction problem'' and the
problem of the singularity in gauge transformation, i.e., ``gauge problem''. In
this paper, we discuss these problems in the Schwarzschild background and
report some recent progress.Comment: 34 pages, 2 figures, submitted to CQG, special volume for Radiation
Reaction (CAPRA7
Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
We derive the analytical solutions of the bound timelike geodesic orbits in
Kerr spacetime. The analytical solutions are expressed in terms of the elliptic
integrals using Mino time as the independent variable. Mino time
decouples the radial and polar motion of a particle and hence leads to forms
more useful to estimate three fundamental frequencies, radial, polar and
azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This
paper gives the first derivation of the analytical expressions of the
fundamental frequencies. This paper also gives the first derivation of the
analytical expressions of all coordinates for the bound timelike geodesics
using Mino time. These analytical expressions should be useful not only to
investigate physical properties of Kerr geodesics but more importantly to
applications related to the estimation of gravitational waves from the extreme
mass ratio inspirals.Comment: A typo in the first expression in equation 21 was fixe
The Japanese space gravitational wave antenna; DECIGO
DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future
Japanese space gravitational wave antenna. DECIGO is expected to open a new window of
observation for gravitational wave astronomy especially between 0.1 Hz and 10 Hz, revealing
various mysteries of the universe such as dark energy, formation mechanism of supermassive
black holes, and inflation of the universe. The pre-conceptual design of DECIGO consists of
three drag-free spacecraft, whose relative displacements are measured by a differential Fabry–
Perot Michelson interferometer. We plan to launch two missions, DECIGO pathfinder and pre-
DECIGO first and finally DECIGO in 2024
DECIGO pathfinder
DECIGO pathfinder (DPF) is a milestone satellite mission for DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) which is a future space gravitational wave antenna. DECIGO is expected to provide us fruitful insights into the universe, in particular about dark energy, a formation mechanism of supermassive black holes, and the inflation of the universe. Since DECIGO will be an extremely large mission which will formed by three drag-free spacecraft with 1000m separation, it is significant to gain the technical feasibility of DECIGO before its planned launch in 2024. Thus, we are planning to launch two milestone missions: DPF and pre-DECIGO. The conceptual design and current status of the first milestone mission, DPF, are reviewed in this article
The status of DECIGO
DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present