International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 201-204
doi:10.1155/S0161171297000252
A hypercontinuous hypersmooth Schwarzschild line element transformation
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.
Abstract
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.