57 research outputs found
Cosmological perturbations on local systems
We study the effect of cosmological expansion on orbits--galactic, planetary,
or atomic--subject to an inverse-square force law. We obtain the laws of motion
for gravitational or electrical interactions from general relativity--in
particular, we find the gravitational field of a mass distribution in an
expanding universe by applying perturbation theory to the Robertson-Walker
metric. Cosmological expansion induces an ( force where
is the cosmological scale factor. In a locally Newtonian framework, we
show that the term represents the effect of a continuous
distribution of cosmological material in Hubble flow, and that the total force
on an object, due to the cosmological material plus the matter perturbation,
can be represented as the negative gradient of a gravitational potential whose
source is the material actually present. We also consider the effect on local
dynamics of the cosmological constant. We calculate the perihelion precession
of elliptical orbits due to the cosmological constant induced force, and work
out a generalized virial relation applicable to gravitationally bound clusters.Comment: 10 page
Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit
We will investigate the influence of the inhomogeneity of the universe,
especially that of the Lema{\^i}tre-Tolman-Bondi (LTB) model, on a
gravitationally bound local system such as the solar system. We concentrate on
the dynamical perturbation to the planetary motion and derive the leading order
effect generated from the LTB model. It will be shown that there appear not
only a well-known cosmological effect arisen from the homogeneous and isotropic
model, such as the Robertson-Walker (RW) model, but also the additional terms
due to the radial inhomogeneity of the LTB model. We will also apply the
obtained results to the problem of secular increase in the astronomical unit,
reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of
the universe cannot have a significant effect for explaining the observed
.Comment: 12 pages, no figure, accepted for publication in Journal of
Astrophysics and Astronom
Acta societatis pro fauna et flora Fennica 71
Kielet saksa, ruotsi ja englanti
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 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 , i.e., ~[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
Suomalaisen eläin- ja kasvitieteellisen seuran Vanamon julkaisuja osa 10
Tiivistelmien kieli suomi
Suomalaisen eläin- ja kasvitieteellisen seuran Vanamon julkaisuja osa 4
Kielet latina, saksa ja suomi
Suomalaisen eläin- ja kasvitieteellisen seuran Vanamon julkaisuja osa 2
Kielet saksa ja suomi
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