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Institut fuer Theoretische Physik
Der Universitaet Goettingen
Bunsenstrasse 9
D 3400 Gottingen


We discuss the problem of degenerate vierbein in the framework of gauge theories of gravitation. We show that a region of space-time with vanishing vierbein but smooth principal connection can be detected by scattering experiments.

August 1982 Referee Report

This paper contains a summary of some of the known aspects of gravity as a gauge theory and addresses, without substantive results, the phenomena associated with regions where the vierbein vanishes. What is new in the paper is connected with this latter question, but I find the discussion misleading and in any case not sufficiently well developed to justify publication in the paperís present form. Coordinate regions where the metric or vierbein vanishes must be treated with considerable care, as there are generally identifications of points to be taken into account. Pictures such as that of Fig. 2 are thus very misleading. The vanishing of the vierbein is not in general a coordinate-independent statement and what seems to be

Two points in one coordinate frame could well be seen to be just one in another. This is the case, e.g., with a uniformly accelerated frame in the x direction, where all points with $X=0$ and $\tau$ finite are to be identified.


December 17, 1984 Comments on the above report:

In retrospect, I realize that the anonymous referee did not, in fact, reject the paper. He suggested that it did not justify publication in its present form. However, I was sufficiently discouraged by his comments to decide not to work on improving the form any further. Also in retrospect, it seems clear that the referee missed my point: when all the information that we have is included in the metric then, we can try to play the game of identifying the points to get rid of the "singularity." But within the framework I was discussing in this paper, there was also a principal connection (as discussed in examples of Hanson-Regge instanton and Einstein-Rosen bridge) using extra dimensions and giving extra-information. Gluing some space-time points together would create discontinuity of the connection. Vierbein, in the paper, was defined as one-form with values in an associated vector bundle and its vanishing was a coordinate independent statement.

Yet, the referee was right on one point: the ideas of the paper could have been developed better. Although I have shied away from the subject in the intervening years, at the time I was suggesting that "faster-than-light teleportation" is possible but, indeed, I failed to provide the explicit description of a transdimensional remolecularizer working on this principle.

Paper in PDF format

Paper in TEX format

Fig. 1

Fig. 2

Last modified on: June 27, 2005.