The absurd thesis "any transformations of the tensor are possible" led to a catastrophic number of errors in the general theory of relativity. (See the book by Landau and Lifshitz Field Theory )

Indeed, such a transformation contradicts the definition of a tensor transformation as a linear transformation. There is no point in translating something if it were known that it is possible to reduce a tensor to any other. In this case, invariants that do not disappear under coordinate transformations and are physical quantities (for example, sizes and angles) disappear.

Thousands of smart people read "Field Theory" in 35 languages ​​and in 12 Russian editions, and no one paid attention to the gross error. Something is wrong when people who consider themselves specialists in GTR repeat the thesis "any transformations of the tensor are possible".

Everything is explained by the observation that the physicist often does not have sufficient knowledge of mathematics and is not familiar with the main works of Einstein:

"Turning to the previous theory of relativity, it is natural to assume under these circumstances that the desired group of transformations must include linear transformations. Consequently, we require that the quantities Г constitute a tensor with respect to arbitrary linear transformations."