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

We revisit the effect of cosmological constant $\Lambda$ on the light deflection and its role in the cosmological lens equation. First, we re-examine the motion of photon in the Schwarzschild spacetime, and explicitly describe the trajectory of photon and deflection angle $\alpha$ up to the second-order in $G$. Then the discussion is extended to the contribution of the cosmological constant $\Lambda$ in the Schwarzschild-de Sitter or Kottler spacetime. Contrary to the previous arguments, we emphasize the following points: (a) the cosmological constant $\Lambda$ does appear in the orbital equation of light, (b) nevertheless the bending angle of light $\alpha$ does not change its form even if $\Lambda \neq 0$ since the contribution of $\Lambda$ is thoroughly absorbed into the definition of the impact parameter, and (c) the effect of $\Lambda$ is completely involved in the angular diameter distance $D_A$.Comment: Revised version accepted for publication in Physical Review D. 5 pages including 3 figures and 4 references are adde

Effect of Gravity on the Macro-Segregation of Larger Steel Ingots

Upon the problem involved in the study of solidification and segregation of larger steel ingots numerous papers have hitherto been published. Nevertheless their nature is still vague from both the scientific and practical points of view. Previous studies have been devoted to the measurement of specific physical values of molten steel, the detailed observation of the sections of solidified ingots, simulat-ion experiments using different materials, experiments on the formation and change of non-metallic inclusions, etc. Isn't there any room for re-examination in these methods of study? Even if these items could be clarified in details, it would not give rise to a satisfactory solut-ion for the phenomenon of ''differential freezing" and to the reduction of segregation and other accompanied defects. We feel much necessity of thorough studies on the solidi-fication and segregation of large steel ingots, before we rush into the epoch of large scale vacuum casting of steel ingots

Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law

We give an idea and the order-of-magnitude estimations to explain the recently reported secular increase of the Astronomical Unit (AU) by Krasinsky and Brumberg (2004). The idea 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. 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, $\frac{d}{dt}{AU} = 15 \pm 4 {(m/cy)}$, the suggested change in the period of rotation of the Sun is about $21 {ms/cy}$ in the case that the orbits of the eight planets have the same "expansion rate." This value is sufficiently 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 change 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. Although the existence of some tidal interactions is assumed between the Sun and planets, concrete mechanisms of the angular momentum transfer are not discussed in this paper, which remain to be done as future investigations.Comment: 4 pages, accepted for publication in PAS

Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity and Gravitatio