Born-Infeld-Einstein theory with matter

TL;DR

This paper derives field equations for a Born-Infeld-Einstein theory with matter, showing how it reproduces Einstein equations for scalar fields and modifies electrodynamics and Dirac equations, with implications for particle size.

Contribution

It introduces a unified approach to include matter in Born-Infeld-Einstein gravity, deriving field equations and analyzing their physical implications, such as finite particle size and modified electrodynamics.

Findings

Scalar field equations match Einstein's with minimal coupling.

Electromagnetic and Dirac equations are reproduced only at lowest order.

Point charges are not allowed; particles must have finite size.

Abstract

The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic and Dirac cases the field equations reproduce the standard equations only to lowest order. The spherically symmetric electrovac equations are studied in detail. It is shown that the resulting Einstein equations correspond to gravity coupled to a modified Born-Infeld theory. It is also shown that point charges are not allowed. All particles must have a finite size. Mass terms for the fields are also considered.