Isotropic Metric in the Theory of General Relativity

TL;DR

This paper advocates for the use of the isotropic metric in general relativity, clarifying its physical interpretation and deriving implications about black holes and the universe's structure.

Contribution

It demonstrates the suitability of the isotropic metric for understanding spatial variables and derives new conclusions about black holes and the universe's topology.

Findings

g_{00} remains non-positive inside black holes

Existence of a universe center if curvature k ≠ 0

Universe is spatially finite but not closed for k > 0

Abstract

We explain why the isotropic metric is quite appropriate to put the physical meaning of spacial variables in the theory of general relativity. Using the isotropic metric, we conclude that i)g_{00} does not become positive even inside the black hole, ii) there exists the center of the Universe if the curvature of the Universe k \ne 0, iii)the Universe is spacially finite but not colsed for k>0.