## Proceedings of the International Conference on Geometry, Integrability and Quantization

### The Dynamics of the Field of Linear Frames and Gauge Gravitation

#### Abstract

The paper is motivated by gauge theories of gravitation and condensed matter, tetrad models of gravitation and generalized Born-Infeld type nonlinearity. The main idea is that any generally-covariant and $\mathrm{GL}(n, \mathbb R)$-invariant theory of the n-leg field (tetrad field when $n=4$) must have the Born-Infeld structure. This means that Lagrangian is given by the square root of the determinant of some second-order twice covariant tensor built in a quadratic way of the field derivatives. It is shown that there exist interesting solutions of the group-theoretical structure. Some models of the interaction between gravitation and matter are suggested. It turns out that in a sense the space-time dimension $n=4$, the normal-hyperbolic signature and velocity of light are integration constants of our differential equations.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436795022

Digital Object Identifier
doi:10.7546/giq-14-2013-201-214

Mathematical Reviews number (MathSciNet)
MR3183940

Zentralblatt MATH identifier
1382.83101

#### Citation

Sławianowski, Jan J.; Martens, Agnieszka. The Dynamics of the Field of Linear Frames and Gauge Gravitation. Proceedings of the Fourteenth International Conference on Geometry, Integrability and Quantization, 201--214, Avangard Prima, Sofia, Bulgaria, 2013. doi:10.7546/giq-14-2013-201-214. https://projecteuclid.org/euclid.pgiq/1436795022