Dynamical Aspects in the Schwarzschild - De Sitter Geometry
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Date
2020-12-01
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Addis Ababa University
Abstract
Within the _CDM model, we studied dynamical aspects of the universe in SdS spacetime background.
Mainly, the precession of orbits from solar-planetary to binary galaxy, the effect of geometry in radially
falling particles to massive compacts and the gravitational deflection of light by extended sources. Using
Einstein field equations and conservation laws, equation of motion and the general effective potential in SdS
were derived. The potential has used in the characterization of the orbits, where hypothetical potential sources
ranging from small mass to critical black holes were used. The sample orbiters cover both massive and massless
particles with and without angular momentum. Generally, SdS potential differs from the Schwarzschild
potential. Moreover, the potential has used to derive important boundary conditions in the motion of the
particles. Specially, it has used to derive photon orbit and radial solution of closed circular orbits of massive
particles. Taking into account the positions of the source, lens and observer the photon orbit solution used to
derive the gravitational bending angle; where it has in turn used in gravitational lensing to estimate the mass of
the lensing where _ effect was of order 2% relative to the Schwarzschild background. In the case of circular
orbits, the radial deviation has studied, where the effect was insignificant at small-scale, within Milky-Way
galaxy; but at binary galaxy level becomes viable, kpc to Mpc order. For the case of elliptical orbits, a
two-body problem has developed to derive the precession. _ effect was dominant over the Schwarzschild
in open and wide systems like binary galaxy, but insignificant in others. _ has significant effect compared
to the Schwarzschild case on radiations from in falling particles to massive objects if appreciable distances
are considered. Finally, we have reflected our views regarding the criticisms on Einstein modified field equations,
attributed to the cosmological constant. A detailed review with some supplementary works presented
to enrich the relevance of the cosmological constant as an intrinsic constant.
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Keywords
Cdm Model, Sds, Cosmological Constant, Orbit Precession, Light Bending, Lensing, Gr