Whether the singularities are removable in some metrics

Abstract

For a long time, the singularities in certain metrics have been problematic and must be removed to avoid unreasonable results in spacetime. Therefore, some new metrics were proposed to eliminate these singularities through coordinate transformations, but they seem not to be workable. In this paper, we re-examine the mathematical structures of the Schwarzschild metric, Reissner-Nordström metric, and Kerr metric. We find that after some transformations, the timelike Eddington-Finkelstein coordinate and the Kruskal-Szekeres coordinates do not delete the singularity problem in the original Schwarzschild metric. It is also true for the tortoise coordinates that it does not solve the singularities at two event horizons in the Kerr metric. After some discussions on those coordinate transformations, a counterexample is given where the singularities are not eliminated.