Masumi Kasai

General Relativistic Effects of Gravity in Quantum Mechanics A Case of Ultra-Relativistic, Spin 1/2 Particles

We present a general relativistic framework for studying gravitational effects in quantum mechanical phenomena. We concentrate our attention on the case of ultra-relativistic, spin1/2 particles propagating in Kerr spacetime. The two-component Weyl equation with general relativistic corrections is obtained in the case of a slowly rotating, weak gravitational field. Our approach is also applied to neutrino oscillations in the presence of a gravitational field. The relative phase of two different mass eigenstates is calculated in radial propagation, and the result is compared with those of previous works.

Secular Increase of the Astronomical Unit : a Possible Explanation in Terms of the Total Angular-Momentum Conservation Law

Aims. We show a possible explanation for the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). Methods. The mechanism proposed is analogous to the tidal acceleration in the Earth-Moon system, which is based on the conservation of the total angular momentum and we apply this scenario to the Sun-planets system. Results. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun and using reported value of the positive secular trend in the astronomical unit, d dt AU = 15±4 (m/cy), the suggested change in the period of rotation of the Sun is about 3 ms/cy in the case that the orbits of the eight planets have the same “expansion rate.” This value is suffi ciently small, and at present it seems there are no observational data which exclude this possibility. Effects of the change in the Sun’s moment of inertia is also investigated. It is pointed out that the ch ange in the moment of inertia due to the radiative mass loss by the Sun may be responsible for the secular increase of AU, if the orbital “expansion” is happening only in the inner planets system.

Effect of the cosmological constant on the bending of light and the cosmological lens equation

Graduate School of Science and Technology, Hirosaki University, Hirosaki, Aomori 036-8561 Japan(Dated: December 26, 2011)We revisit the effect of cosmological constant Λ on the light deflection and its role in the cosmolog-ical lens equation. First, we re-examine the motion of photon in the Schwarzschild spacetime, andexplicitly describe the trajectory of photon and deflection angle αup to the second-order in G. Thenthe discussion is extended to the contribution of the cosmological constant Λ in the Schwarzschild-deSitter or Kottler spacetime. Contrary to the previous arguments, we emphasize the following points:(a) the cosmological constant Λ does appear in the orbital equation of light, (b) nevertheless thebending angle of light αdoes not change its form even if Λ 6= 0 since the contribution of Λ is thor-oughly absorbed into the definition of the impact parameter, and (c) the effect of Λ is completelyinvolved in the angular diameter distance D

Toward a No-Go Theorem for an Accelerating Universe through a Nonlinear Backreaction

The backreaction of nonlinear inhomogeneities to the cosmic expansion is re-analyzed in the framework of general relativity. Apparent discrepancies regarding the effect of the nonlinear backreaction, which exist among the results of previous works in different gauges, are resolved. By defining the spatially averaged matter energy density as a conserved quantity in the large comoving volume, it is shown that the nonlinear backreaction neither accelerates nor decelerates the cosmic expansion in a matter-dominated universe. The present result in the Newtonian gauge is consistent with the previous results obtained in the comoving synchronous gauge. Although our work does not give a complete proof, it strongly suggests the following no-go theorem: No cosmic acceleration occurs as a result of the nonlinear backreaction via averaging.

An Analytical Approximation of the Luminosity Distance in Flat Cosmologies with a Cosmological Constant

We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is written simply in terms of a rational function. We also show the approximate formulae for the Dyer-Roeder distance (empty beam case) and the generalized angular diameter distance from redshift

Apparent Acceleration through Large-Scale Inhomogeneities Post-Friedmannian Effects of Inhomogeneities on the Luminosity Distance

z_1

Can We See a Rotating Gravitational Lens

to

Non-Linear Vorticity-Density Coupling in Lagrangian Dynamics

z_2

Angular diameter distance in a clumpy universe

, which are particularly useful in analyzing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter

The number count - redshift relation in a perturbed Friedmann universe

0.3 \leq \Omega_{\rm m} \leq 1