A heuristic solution for the Pioneer anomaly employing an ELA metric with dark matter in the outskirts of the Solar system

Abstract

Considering an expanding locally anisotropic (ELA) metric with the Sun as central mass and the heuristic ansatz for the dimensionless functional exponent parameter 'alpha=3+alpha_2(r_1)(1-U_Sun)^2' with a linear ansatz 'alpha_2(r_1)=alpha_2^(2.0)+alpha_2^(2.1) r_1' above 20 AU the pioneer anomaly is fully accounted for as due to the blue-shift of the background space-time. For compatibility with orbital motion within the Solar system it is further considered a branch ansatz for which \alpha_2(r_1)=0 below 20 AU. This construction reduces the physical acceleration correction above 20 AU down to ~10^(-14) m/s^2 outwards from the Sun such that orbital corrections to Neptune and Pluto are less notorious than when the full Pioneer acceleration is considered to be a gravitational acceleration. It is also discussed the effective mass-energy density distribution above 20 AU due to the background corrections, the respective equation of state ('-1 < w < -0.726') and the finite non-null total mass is computed by considering an upper cut-off for the functional parameter 'alpha'. Such effective extended configuration is tentatively interpreted as a cold dark matter distribution.