Relativity and Cosmology

   

Effects of Coordinate Curvature on Integration

Authors: C. A. Laforet

In this paper, the integration of a function over a curved manifold is examined in the case where the curvature of the manifold results in a varying density of coordinates over which the function is being integrated where the upper bound of the of integration is infinity. It is shown that when the coordinate density varies in such a case, the true area under the curve is not correctly calculated by traditional techniques of integration. This situation is then applied to the Schwarzschild metric and geodesic equation of General Relativity to examine the proper time taken for a freefalling observer to reach the event horizon of a black hole.

Comments: 10 Pages.

Download: PDF

Submission history

[v1] 2017-07-05 14:31:07
[v2] 2017-07-06 09:26:52
[v3] 2017-07-26 11:06:39

Unique-IP document downloads: 45 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus