2013/03/25 by Jan Jerzy Sławianowski, Vasyl Kovalchuk, Sławianowski, Jan Jerzy +7
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1304.0736
41 pages
arxiv created 2016/02/17 · arxiv updated 2016/02/18
It is well known that there are various models of gravitation: the metrical Hilbert-Einstein theory, a wide class of intrinsically Lorentz-invariant tetrad theories (of course, generally-covariant in the space-time sense), and many gauge models based on various internal symmetry groups (Lorentz, Poincare, \rm GL(n,ℝ), \rm SU(2,2), \rm GL(4,ℂ), and so on). One believes usually in gauge models and we also do it. Nevertheless, it is an interesting idea to develop the class of \rm GL(4,ℝ)-invariant (or rather \rm GL(n,ℝ)-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 idea 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 non-accidental 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. It is also interesting that within such 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.