Universality of affine formulation in General Relativity theory

TL;DR

This paper discusses the affine variational principle in General Relativity, highlighting its advantages over the metric formulation, especially in simplifying the theory's structure and aiding quantization.

Contribution

It demonstrates the universality of the affine formulation in General Relativity and its benefits in handling boundary integrals and simplifying the canonical structure.

Findings

Affine formulation avoids non-universal properties of the metric version.

It simplifies the canonical structure of the theory.

Provides a straightforward method for boundary integrals in GR.

Abstract

Affine variational principle for General Relativity, proposed in 1978 by one of us (J.K.), is a good remedy for the non-universal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric derivatives. Affine version of the theory cures the standard drawback of the metric version, where the leading (second order) term of the field equations depends upon matter fields and its causal structure violates the light cone structure of the metric. Choosing the affine connection (and not the metric one) as the gravitational configuration, simplifies considerably the canonical structure of the theory and is more suitable for purposes of its quantization along the lines of Ashtekar and Lewandowski (see http://www.arxiv.org/gr-qc/0404018). We show how the affine formulation provides a simple method to handle boundary integrals in general relativity theory.