Newtonian wormholes

TL;DR

This paper introduces a Newtonian gravity-based wormhole solution in curved space, analyzing particle dynamics and suggesting the potential existence of Newtonian black holes, thus extending classical gravity concepts.

Contribution

It presents a novel Newtonian wormhole model with detailed geometric and dynamical analysis, including the possibility of Newtonian black holes, which is a new concept in classical gravity.

Findings

Wormhole solution in Newtonian gravitation with a curved space geometry.

Analysis of particle motion reveals three distinct radii in circular orbits.

A limiting case hints at the theoretical possibility of Newtonian black holes.

Abstract

A wormhole solution in Newtonian gravitation, enhanced through an equation relating the Ricci scalar to the mass density, is presented. The wormhole inhabits a spherically symmetric curved space, with one throat and two asymptotically flat regions. Particle dynamics in this geometry is studied, and the three distinct dynamical radii, namely, the geodesic, circumferential, and curvature radii, appear naturally in the study of circular motion. Generic motion is also analysed. A limiting case, although inconclusive, suggests the possibility of having a Newtonian black hole in a region of finite (nonzero) size.