Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers

The concept of coordinate transformation is fundamental to the theory of differentiable manifolds, which in turn plays a central role in many modern physical theories. The notion of metric extension is also important in these respects. In this short note we provide some simple examples illustrating these concepts, with the intent of alleviating the confusion that often arises in their use. While the examples themselves can be considered unrelated to the theory of general relativity, they have clear implications for the results cited in a number of recent publications dealing with the subject. These implications are discussed