Pseudo-Newtonian gravitational potential for Schwarzschild-de Sitter spacetimes

TL;DR

This paper introduces a pseudo-Newtonian potential for Schwarzschild-de Sitter spacetimes, enabling simpler modeling of black hole environments with a cosmological constant, useful for astrophysical applications like accretion discs.

Contribution

A new pseudo-Newtonian potential is developed and validated for Schwarzschild-de Sitter black holes, bridging Newtonian and relativistic descriptions in cosmological contexts.

Findings

The pseudo-Newtonian potential closely matches relativistic effective potentials.

The approach is effective for cosmological parameters y<10^{-6}.

Potential applications include modeling accretion discs in large galactic structures.

Abstract

Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test-particle motion is constructed and compared with its general relativistic counterpart given by the Schwarzschild-de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion discs in astrophysically interesting situations in large galactic structures for the Schwarzschild-de Sitter spacetimes with the cosmological parameter y=(1/3)\Lambda M^2<10^{-6}.