Space‐time as a structured relativistic continuum

DOI10.1002/MMA.5087zbMATH Open1407.83004arXiv1304.0736OpenAlexW2963295528WikidataQ129732669 ScholiaQ129732669MaRDI QIDQ4685541

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Publication date: 9 October 2018

Published in: (Search for Journal in Brave)

Abstract: 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, $mGL(n,mathbbR)$, $mSU(2,2)$, $mGL(4,mathbbC)$, 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 $mGL(4,mathbbR)$-invariant (or rather $mGL(n,mathbbR)$-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.

Full work available at URL: https://arxiv.org/abs/1304.0736

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