Eur. Phys. J. Plus (2021) 136: 71
https://doi.org/10.1140/epjp/s13360-020-01002-6

Regular Article

The modified Newton attraction law and its connection with cosmological $\Lambda$ term

¹ Keldysh Institute of Applied Mathematics of RAS, Miusskaya sq., 4, 125047, Moscow, Russia
² Institute of Computer Aided Design of RAS, 2nd Brestskaya st., 19/18, 123056, Moscow, Russia

^a oberon@kiam.ru

Received: 30 October 2020
Accepted: 8 December 2020
Published online: 12 January 2021

Abstract

We consider the possibility of generalizing the Newtonian law of gravity and the transition to a general relativistic model for weak fields with the inclusion of a repulsive term identified as a cosmological constant. The analysis includes that of the test particle’s motion in a modified gravitational field of the Hilbert metric and then the problem of the reverse transition from the post-Galilean case to the construction of a modified exact point mass metric which includes the $\Lambda$ term.