Universality of affine formulation in general relativity

The affine variational principle for general relativity, proposed in 1978 by one of us, is a good remedy for the nonuniversal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric derivatives. The 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 the 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 the purposes of its quantization along the lines of Ashtekar and Lewandowski. We show how the affine formulation provides a simple method to handle boundary integrals in general relativity theory.