A Strengthening of the Lovelock-Theorem: the Einstein Field Equation is Valid in ALL Dimensions, not Just 4

A Strengthening of the Lovelock-Theorem: the Einstein Field Equation is Valid in ALL Dimensions, not Just 4 The standard argument for the uniqueness of the Einstein field equation is based on
Lovelock’s Theorem, the relevant statement of which is restricted to four dimensions. I
prove a theorem similar to Lovelock’s, with a physically modified assumption: that the
geometric object representing curvature in the Einstein field equation ought to have the
physical dimension of stress-energy. The theorem is stronger than Lovelock’s in two ways:
it holds in all dimensions, and so supports a generalized argument for uniqueness; it does
not assume that the desired tensor depends on the metric only up second-order partialderivatives,
that condition being a consequence of the proof. This has consequences for
understanding the nature of the cosmological constant and theories of higher-dimensional
gravity. Another consequence of the theorem is that it makes precise the sense in which
there can be no gravitational stress-energy tensor in general relativity. Along the way, I
prove a result of some interest about the second jet-bundle of the bundle of metrics over
a manifold.