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arXiv · 2509.02490

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

Arian L. von Blanckenburg·Domenico Giulini·Philip K. Schwartz
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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.

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Arian L. von Blanckenburg, Domenico Giulini, Philip K. Schwartz. 2025-09-02. The trace-free Einstein tensor is not variational for the metric as field variable. https://doi.org/10.1088/1361-6382/ae4709

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