An analysis of Born-Infeld determinantal gravity in Weitzenbock spacetime

TL;DR

This paper explores Born-Infeld gravity formulated in Weitzenbock spacetime, showing it reduces to Einstein gravity in the low field limit and discussing its properties and solutions like Schwarzschild geometry.

Contribution

It provides a detailed analysis of Born-Infeld determinantal gravity in Weitzenbock spacetime, deriving equations of motion and linking them to Einstein gravity with a purely geometrical energy-momentum tensor.

Findings

Equations of motion resemble Einstein's gravity plus a geometrical energy-momentum tensor.

In the low field limit, the theory reduces to Einstein gravity.

Schwarzschild geometry naturally emerges in the spherical symmetry case.

Abstract

The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born-Infeld constant goes to infinity, and it is described by second order field equations for the vielbein field in $D$ spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativity plus an energy-momentum tensor of purely geometrical character. This tensor is obtained solely from the parallelization defining the spacetime structure, which is encoded in a set of D smooth, everywhere non-null, globally defined 1-forms. Spherical symmetry is studied as an example, and we comment on the emergence of the Schwarzschild geometry within this framework. Potential (regular) extensions of it are envisioned.