Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008ap%26ss.317..139m&link_type=abstract
Astrophysics and Space Science, Volume 317, Issue 1-2, pp. 139-141
Mathematics
Logic
5
Variable Cosmological Constant, Geodesic Motion, Field Equations Of Gravity, Pioneer Anomaly
Scientific paper
We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ( x i ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ∂Λ/ ∂ x i and, in the weak field approximation, causes an anomalous acceleration A˜( Vc 2/ γ ρ) ∂Λ/ ∂ t+( c 4/ γ ρ) ∂Λ/ ∂ r where V= dr/ dt, c=the speed of light, γ=8 π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ( t) give A<10-8 cm/s2 when ρ>10-29 g/cm3 i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.
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