On the naturalness of Einstein's equation

Details On the naturalness of Einstein's equation On the naturalness of Einstein's equation

2007-09-12

arxiv.org/abs/0709.1928v2

J Geom. Phys. 58, 8 (2008) 1007-1014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, added references, corrected typos

Scientific paper

10.1016/j.geomphys.2008.03.007

We compute all 2-covariant tensors naturally constructed from a semiriemannian metric which are divergence-free and have weight greater than -2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the unit of scale). Since these two conditions are also satisfied by the energy-momentum tensor of a relativistic space-time, we discuss in detail how these theorems lead to the field equation of General Relativity.

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