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Hideki Asada

Publications and source records attributed to Hideki Asada.

96 records · Page 6Linked to original sources
arXiv1998

Formulation for the internal motion of quasi-equilibrium configurations in general relativity

We present a formulation for the internal motion of equilibrium configurations with a rotational Killing vector in general relativity. As an approximation, this formulation is applicable to investigation of the internal motion of quasi-equilibrium configurations such as binary neutron stars. Based on this simple formulation, a condition for the general relativistic counter rotation has been obtained, though in the recent work by Bonazzola, Gourgoulhon and Marck, their condition for the counter rotation is not enough to specify the internal velocity field. Under the condition given in this paper, the internal velocity field can be determined completely. Indeed, in the counter-rotating case, we have also derived Poisson equations for the internal velocity, which take tractable forms in numerical implementation.

gr-qc↗
arXiv1998

Observation of Gravitational Lensing in the Clumpy Universe

We discuss how inhomogeneities of the universe affect observations of the gravitational lensing; (1) the bending angle, (2) the lensing statistics and (3) the time delay. In order to take account of the inhomogeneities, the Dyer-Roeder distance is used, which includes a parameter representing the clumpiness of the matter along the line of sight. It is shown analytically that all three combinations of distances appearing in the above observations (1)-(3) are monotonic with respect to the clumpiness in general, for any given set of the density parameter, cosmological constant and redshifts of the lens and the source. Some implications of this result for the observation are presented; the clumpiness decreases both the bending angle and the lensing event rate, while it increases the time delay. We also discuss cosmological tests using the gravitational lensing in the clumpy universe.

astro-ph↗
arXiv1996

Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters

We investigate the cosmological test recently proposed by B. Fort, Y. Mellier and M. Dantel-Fort (FMD), where the observed location of the critical line in gravitational lensing is used to determine the cosmological parameters, $Ω$ and $λ$. Applying this method to the cluster of galaxies Cl0024+1654, FMD obtained a constraint on the cosmological constant, $λ> 0.6$, assuming the spatially flat universe. It plays a crucial role in this method that the angular diameter distance-redshift relation depends on the cosmological models through the cosmological parameters. First, using the angular diameter distance in the Friedmann-Lemaitre- Robertson-Walker universe, we show that one can hardly determine $Ω$ by this method without the assumption of the spatially flat universe. We also investigate the effect of inhomogeneities of the universe by using the Dyer-Roeder angular diameter distance. It is shown that the effect of inhomogeneities can become too large to be ignored, particularly for a high density universe. As a result, this method cannot be taken as a clear cosmological test to determine $Ω$ and $λ$, though it may provide a bound on $Ω$ and $λ$. Moreover, we mention the uncertainty of the determination of the velocity dispersion, which is regarded as one of the most serious problems in this test.

astro-ph↗
arXiv1996

Formulation for nonaxisymmetric uniformly rotating equilibrium configurations in the second post-Newtonian approximation of general relativity

We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms decrease rapidly enough at the external region of the matter(i.e., at worst $O(r^{-4})$). Hence these Poisson equations can be solved accurately as the boundary value problem using standard numerical methods.This formalism will be useful to obtain nonaxisymmetric uniformly rotating equilibrium configurations such as synchronized binary neutron stars just before merging and the Jacobi ellipsoid.

gr-qc↗
arXiv1996

Post-Newtonian Hydrodynamic Equations Using the (3+1) Formalism in General Relativity

Using the (3+1) formalism in general relativity, we perform the post-Newtonian(PN) approximation to clarify what sort of gauge condition is suitable for numerical analysis of coalescing compact binary neutron stars and gravitational waves from them. We adopt a kind of transverse gauge condition to determine the shift vector. On the other hand, for determination of the time slice, we adopt three slice conditions(conformal slice, maximal slice and harmonic slice) and discuss their properties. Using these conditions, the PN hydrodynamic equations are obtained up through the 2.5PN order including the quadrupole gravitational radiation reaction. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. It is found that the conformal slice seems appropriate for analysis of gravitational waves in the wave zone and the maximal slice will be useful for describing the equilibrium configurations. The PN approximation in the (3+1) formalism will be also useful to perform numerical simulations using various slice conditions and, as a result, to provide an initial data for the final merging phase of coalescing binary neutron stars which can be treated only by fully general relativistic simulations.

gr-qc↗