I would love to discuss in another thread perhaps why I think this is so, but for now it seems more worthwhile to go over what I make out to be the main claims of Crothers and why I either agree or disagree with those claims.

Thank you. I have something to add to your third note.


3. He claims that the r in the Schwarzschild solution is the curvature of radius.

Agreed. Calculated it myself and it is. How much emphasis you put into the significance of this fact is up for debate I suppose though.

The radial coordinate r is defined in terms of the area of a 2-sphere that's symmetric around the central singularity; it is not defined as the Euclidean distance from that singularity to the 2-sphere.

That fact is acknowledged by standard textbooks. In Misner/Thorne/Wheeler, r is defined by equation (23.9'). In Wald, r is defined by equation (6.1.3). As Wald wrote:

Robert M Wald:

In flat, three-dimensional Euclidean space, r would also be the value of the radius of the sphere, i.e., the distance from the surface of the sphere to its center. However, in a curved space, a sphere need not have a center...and even if it does, r need not bear any relation to the distance to the center. Nevertheless, we shall refer to r as the "radial coordinate" of the sphere.

MTW's and Wald's textbooks were published long before Crothers published his first paper. When Crothers writes things like

Stephen J Crothers:

None of the relativists have understood this, including Einstein himself.

he is either ignorant or lying. Crothers has written things like that in just about every paper he's published. (The quotation above comes from "A brief history of black holes", which I cited in the OP and again in post #18.)

This is an HTML translation of something I wrote in March 2012 concerning the mathematics of black hole denialism at the online forum now known as the Internation Skeptics Forum. The original forum posts are still online, but that forum no longer renders equations (LaTeX) correctly. For this translation to HTML, I have replaced LaTeX by images and made a few small corrections and deletions. For context and an index, see my introduction to this material.

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