On isotropic metric of Schwarzschild solution of Einstein equation

TL;DR

This paper introduces a new dynamic and periodic isotropic metric for the Schwarzschild solution that extends beyond the traditional range, featuring infinite singularities and allowing for arbitrary small r0, challenging previous limitations.

Contribution

A novel isotropic metric for Schwarzschild spacetime that is dynamic, periodic, and extends the coordinate range beyond the classical solution.

Findings

The new metric is dynamic and periodic.

It contains infinite spacetime singularities.

It extends the coordinate range beyond r=2MG, including negative r regions.

Abstract

The known static isotropic metric of Schwarzschild solution of Einstein equation cannot cover with the range of r<2MG, a new isotropic metric of Schwarzschild solution is obtained. The new isotropic metric has the characters: (1) It is dynamic and periodic. (2) It has infinite singularities of the spacetime. (3) It cannot cover with the range of 0<r<r0; On the other hand, r0 can be small discretionarily. (4) It seemed as if the range of negative r could be unavoidable, although this range is meaningless for the Schwarzschild metric.