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Solar system effects in Schwarzschild--de Sitter spacetime

Valeria Kagramanova·Jutta Kunz·Claus Lämmerzahl
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Abstract

The Schwarzschild--de Sitter space--time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant $Λ$. Based on this space--time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, Perihelion shift, geodetic or de Sitter precession, as well as the influence of $Λ$ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For $Λ=Λ_0 \sim 10^{-52} {\rm m}^{-2}$ the cosmological constant plays no role for all of these effects, while a value of $Λ\sim - 10^{-37} {\rm m}^{-2}$, if hypothetically held responsible for the Pioneer anomaly, is not compatible with the Perihelion shift.

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Valeria Kagramanova, Jutta Kunz, Claus Lämmerzahl. 2006-03-18. Solar system effects in Schwarzschild--de Sitter spacetime. https://doi.org/10.1016/j.physletb.2006.01.069

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