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.
Highlights
In [I], the linear effect line element is derived and, in [2], a general llne element d$’ is derived by considering a non-reversible P-process emanating from the center of a spherical conflguratlon and its interaction with the substratum. This interaction is modeled by taking the Special Theory chronotopic interval and modifying its spherical coordinate transformation by a type of damping of the basic light-clock counts
This damping is characterized by the two expressions (i) dR"
In arguing for the use of the transformed Schwarzschild line element (1.1), Lawden assumes that it is possible for R" 2GM/c But the assumed real valued function defined by equation 57.11 is not defined for R" such that R 2GM/c2
Summary
In [I], the linear effect line element is derived and, in [2], a general llne element d$’ is derived by considering a non-reversible P-process emanating from the center of a spherical conflguratlon and its interaction with the substratum. The following general line element is derived. In arguing for the use of the transformed Schwarzschild line element (1.1), Lawden assumes that it is possible for R" 2GM/c But the assumed real valued function defined by equation 57.11 is not defined for R" such that R 2GM/c2.
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