The trace-free Einstein tensor is not variational for the metric as field variable

Abstract

It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse) metric as field variable. We show that this statement remains true even for general local actions, without the assumption of diffeomorphism invariance.

Theorems & Definitions (4)

• Theorem 1
• Theorem 2: informal statement
• Theorem 3: informal statement
• proof : Proof of \ref{['thm:non-var']}