A New Solution of Einstein Vacuum Field Equations

TL;DR

This paper introduces a novel, singularity-free vacuum solution to Einstein's equations that generalizes the Ozsvath-Schucking solution, revealing hidden curvature sources and offering a Machian perspective.

Contribution

It presents a new vacuum solution with a vanishing Kretschmann scalar, generalizing previous solutions and providing a method to identify curvature sources via dimensional parameters.

Findings

Solution is singularity-free despite being curved

Curvature source can be expressed through dimensional parameters

Generalizes the Ozsvath-Schucking solution

Abstract

A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new solution has a vanishing Kretschmann scalar and is singularity-free despite being curved. The discovery of the new solution is facilitated by a new insight which reveals that it is always possible to define the source of curvature in a vacuum solution in terms of some dimensional parameters. As the parameters vanish, so does the curvature. The new insight also helps to make the vacuum solutions Machian.