Teleparallelism, modified Born-Infeld nonlinearity and space-time as a micromorphic ether

TL;DR

This paper explores a field-theoretic model with GL(n,R) invariance that links Einstein-like equations, Born-Infeld nonlinearity, and the relativistic mechanics of structured continua, revealing vacuum solutions related to semisimple Lie groups.

Contribution

It introduces a covariant, GL(n,R)-invariant model connecting Einstein theory, Born-Infeld nonlinearity, and structured continuum mechanics, with signature emerging from integration constants.

Findings

Field equations resemble Einstein's equations.

Existence of homogeneous vacuum solutions linked to Lie groups.

Connection established between Born-Infeld nonlinearity and relativistic mechanics.

Abstract

Discussed are field-theoretic models with degrees of freedom described by the $n$-leg field in an $n$-dimensional "space-time" manifold. Lagrangians are generally-covariant and invariant under the internal group GL$(n,{\bf R})$. It is shown that the resulting field equations have some correspondence with Einstein theory and possess homogeneous vacuum solutions given by semisimple Lie group spaces or their appropriate deformations. There exists a characteristic link with the generalized Born-Infeld type nonlinearity and relativistic mechanics of structured continua. In our model signature is not introduced by hands, but is given by integration constants for certain differential equations.