| Abstract: | There are various models of gravitation: the metrical Hilbert‐Einstein theory, a wide class of intrinsically Lorentz‐invariant tetrad theories (generally covariant in the space‐time sense), and many gauge models based on various internal symmetry groups (Lorentz, Poincare,  , etc). The gauge models are usually preferred but nevertheless it is an interesting idea to develop the class of  ‐invariant (or rather  ‐invariant) tetrad (n‐leg) generally covariant models. This is done below and motivated by our idea of bringing back to life the Thales of Miletus concept of affine symmetry. Formally, the obtained scheme is a generally covariant tetrad (n‐leg) model, but it turns out that generally covariant and intrinsically affinely invariant models must have a kind of nonaccidental Born‐Infeld‐like structure. Let us also mention that they, being based on tetrads (n‐legs), have many features common with continuous defect theories. It is interesting that they possess some group‐theoretical solutions and more general spherically symmetric solutions, discussion of which is the main new result presented in this paper, including the applications of the 't Hooft‐Polyakov monopoles in the generally covariant theories, which enables us to find some rigorous solutions of our strongly nonlinear equations. It is also interesting that within such a framework, the normal‐hyperbolic signature of the space‐time metric is not introduced by hand but appears as a kind of solution, rather integration constants, of differential equations. Let us mention that our Born‐Infeld scheme is more general than alternative tetrad models. It may be also used within more general schemes, including also the gauge ones. |
