https://arxiv.org/abs/1708.07404

For almost 170 years it is known that, in multivariate calculus, for coordinate transformations, say x,y→u,v, one has dxdy=Jdudv, where J is the appropriate Jacobian. Essentially by using this fundamental mathematical rule, it was shown that "Schwarzschild Singularity" is actually a point singularity as shown earlier (Bel, JMP 10, 1051, 1969) and suggested even earlier (Janis, Newman, and Winicour, PRL 20, 878, 1968). However recently Kundu (arXiv:1706.07463) has claimed that this 170 year old Jacobi rule is incorrect. First, we show that the Jacobi rule is indeed correct. The easiest way to verify this is to note that in 2-D polar coordinates, volume element dV=rdrdθ=rdθdr=dxdy=dydx, involves ordinary symmetric products. We also how several independent proofs to support the result that, for a neutral point mass (and not for extended bodies), the gravitational mass M=0.

Physically, for a point mass at R=0, one expects Ric∼Mδ(R=0) (Narlikar \& Padmanabhan, Found. Phys., 18, 659, 1988). But the black hole solution is obtained from Ric=0. Again this is the most direct proof that M=0 for a Schwarzschild black hole. Implication of this result is that the observed massive black hole candidates are non-singular quasi black holes or black hole mimickers which can possess strong magnetic fields as has been observed.