Abstract:
We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.

Abstract:
Krasinsky and Brumberg (2004 Celest. Mech. Dyn. Astron., 90, 267) reported a secular increase of the astronomical unit (AU) of 15 meters per century. Recently, Miura et al. (2009, PASJ, 61) proposed that a possible angular momentum transfer from the rotation of the Sun to the orbital motion of the solar system planets may explain the observed increase of the AU. They assumed that the tidal effect between the planets and the Sun is the cause of this transfer. Here we claim that tidal effect cannot be a cause of this type of the transfer to explain the increase of the AU.

Abstract:
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3 PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5 PN radiation reaction effect), is Lorentz invariant and is unambiguous: there exist no undetermined parameter reported in the previous works. We shall show that our 3 PN equation of motion agrees physically with the Blanchet and Faye 3 PN equation of motion if $\lambda = - 1987/3080$, where $\lambda$ is the parameter which is undetermined within their framework. This value of $\lambda$ is consistent with the result of Damour, Jaranowski, and Sch\"afer who first completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the dimensional regularization.

Abstract:
A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle limit enables us to incorporate a notion of a self-gravitating regular star into general relativity. The resulting 3 PN equation of motion is Lorentz invariant, unambiguous, and conserves an energy of the binary orbital motion.

Abstract:
We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

Abstract:
The space of phase-parameters (sky-position, frequency, spindowns) of a coherent matched-filtering search for continuous gravitational waves from isolated neutron stars shows strong global correlations (``circles in the sky''). In the local limit this can be analysed in terms of a parameter-space metric, but the global properties are less well studied. In this work we report on our recent progress in understanding these global correlations analytically for short to intermediate (less than a month, say) observation times and neglecting spindowns. The location of these correlation-circles in parameter-space is found to be determined mostly by the orbital velocity of the earth, while the spin-motion of the detector and the antenna-patterns only contribute significantly to the amplitude of the detection statistic along these circles.

Abstract:
A third post-Newtonian (3 PN) equation of motion for an inspiralling binary consisting of two spherical compact stars with strong internal gravity is derived under harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in a sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3 PN equation of motion and an energy of the binary orbital motion in case of the circular orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of the mass frame. It is argued that the 3 PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.

Abstract:
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves. Long wavelength of gravitational waves and compactness of possible sources may enable us to extract information in the interference among the lensed images. We point out that the interference term contains information of relative transverse velocity of the source-lens-observer system, which may be obtained by possible future space-borne gravitational wave detectors such as BBO/DECIGO.

Abstract:
The peculiar motion of the Earth causes a dipole anisotropy modulation in the distant galaxy distribution due to the aberration effect. However, the amplitude and angular direction of the effect is not necessarily the same as those of the cosmic microwave background (CMB) dipole anisotropy due to the growth of cosmic structures. In other words exploring the aberration effect may give us a clue to the horizon-scale physics perhaps related to the cosmic acceleration. In this paper we develop a method to explore the dipole angular modulation from the pixelized galaxy data on the sky properly taking into account the covariances due to the shot noise and the intrinsic galaxy clustering contamination as well as the partial sky coverage. We applied the method to the galaxy catalogs constructed from the Sloan Digital Sky Survey (SDSS) Data Release 6 data. After constructing the four galaxy catalogs that are different in the ranges of magnitudes and photometric redshifts to study possible systematics, we found that the most robust sample against systematics indicates no dipole anisotropy in the galaxy distribution. This finding is consistent with the expectation from the concordance Lambda-dominated cold dark matter model. Finally we argue that an almost full-sky galaxy survey such as LSST may allow for a significant detection of the aberration effect of the CMB dipole having the precision of constraining the angular direction to ~ 20 degrees in radius. Assuming a hypothetical LSST galaxy survey, we find that this method can confirm or reject the result implied from a stacked analysis of the kinetic Sunyaev-Zel'dovich effect of X-ray luminous clusters in Kashlinsky et al. (2008,2009) if the implied cosmic bulk flow is not extended out to the horizon.

Abstract:
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a non-rotating spherical object which is consisitent with previous studies.