International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 201-204

A hypercontinuous hypersmooth Schwarzschild line element transformation

Robert A. Herrmann

Mathematics Department, United States Naval Academy, 572 Holloway Rd., Annapolis 21402-5002, MD, USA

Received 3 April 1995; Revised 21 June 1995

Copyright © 1997 Robert A. Herrmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that is modeled by an ideal nonstandard physical world transformation process that yields a connection between an exterior Schwarzschild line element and distinctly different interior line element. The transformation is an ideal transformation in that in the natural world the transformation is conceived of as occurring at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzsclfild radius. An ideal transformation models this transformation in a manner independent of the objects standard radius. It yields predicted behavior based upon a Newtonian gravitational field prior to the transformation, predicted behavior after the transformation for a field internal to the Schwarzschild surface and predicted behavior with respect to field alteration processes during the transformation.