caa a22 4500 445387149 CHVBK 20180317143035.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10714-011-1170-1 doi (NATIONALLICENCE)springer-10.1007/s10714-011-1170-1 Arakida Hideyoshi School of Education, Waseda University, 1-6-1, Nishiwaseda, Shinjuku, 169-8050, Tokyo, Japan aut Application of time transfer function to McVittie spacetime: gravitational time delay and secular increase in astronomical unit [Elektronische Daten] [Hideyoshi Arakida] 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-Lemaître-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte etal. (Class Quantum Gravity 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class Quantum Gravity 25:145020, 2008), which is originally related to Synge's world function Ω(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 dAU/dt, i.e., 15 ± 4 (m/century). Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion. Springer Science+Business Media, LLC, 2011 Gravitation nationallicence Relativity nationallicence Ephemerides nationallicence Astronomical unit nationallicence Light propagation nationallicence General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/8(2011-08-01), 2127-2139 0001-7701 43:8<2127 2011 43 10714 https://doi.org/10.1007/s10714-011-1170-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-011-1170-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Arakida Hideyoshi School of Education, Waseda University, 1-6-1, Nishiwaseda, Shinjuku, 169-8050, Tokyo, Japan aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/8(2011-08-01), 2127-2139 0001-7701 43:8<2127 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer