Curious interior solutions of general relativity

TL;DR

This paper explores a class of exact static spherically symmetric vacuum solutions in general relativity by matching interior and exterior metrics in different gauges, providing a unified manifold framework.

Contribution

It introduces a novel method of constructing composite solutions by matching Schwarzschild and isotropic gauges at a junction surface, unifying different coordinate representations.

Findings

Successfully constructs composite vacuum solutions with matched interior and exterior metrics.

Provides a rigorous framework linking different gauges within a single differentiable manifold.

Enhances understanding of static spherically symmetric solutions in Einstein's equations.

Abstract

In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric in Schwarzschild original gauge, to the exterior vacuum metric in isotropic gauge, at a junction surface. This approach allows us to associate rigorously with both gauges as a same "space", which is a unique differentiable manifold M^4