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

TL;DR

This paper explores a generalized Newtonian gravity law incorporating a cosmological constant, connecting it with relativistic models and analyzing particle motion in modified gravitational fields.

Contribution

It introduces a modified Newtonian gravity law with a $ ext{Lambda}$-term and constructs a corresponding exact point mass metric, bridging Newtonian and relativistic gravity.

Findings

Derived a modified gravitational law including the $ ext{Lambda}$-term.

Analyzed test particle motion in the modified gravitational field.

Constructed a modified exact point mass metric with the $ ext{Lambda}$-term.

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.