Universality of the Einstein theory of gravitation

TL;DR

This paper proves that all generalized theories of gravity based on scalar densities involving the metric and curvature are essentially equivalent to Einstein's theory, possibly with a different metric and matter fields, using a novel variational approach.

Contribution

It introduces a new method for variational problems that shows the universality of Einstein's theory among a broad class of gravitational models.

Findings

Generalizations of general relativity are equivalent to Einstein's theory with a different metric.

The proof relies on a new approach to variational problems involving metric and connection.

The result demonstrates the fundamental uniqueness of Einstein's gravitational theory.

Abstract

We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian $L_{Hilbert} = \frac 1{16\pi} \sqrt{|g|} R$ by a generic scalar density $L=L(g_{\mu\nu}, R^\lambda_{\mu\nu\kappa})$ depending upon the metric $g_{\mu\nu}$ and the curvature tensor $R^\lambda_{\mu\nu\kappa}$, are equivalent to the conventional Einstein theory for a (possibly) different metric tensor $\tilde{g}_{\mu\nu}$ and (possibly) a different set of matter fields. The simple proof of this theorem relies on a new approach to variational problems containing metric and connection.