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

Classical and Quantum Gravity 2026 Open access

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Authors: Arian L. von Blanckenburg, Domenico Giulini, Philip K. Schwartz
DOI: 10.1088/1361-6382/ae4709
Cited by: 0
References: 10

Abstract

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Cosmology and Gravitation Theories

Publication details

Journal / source
Classical and Quantum Gravity
Publisher
IOP Publishing
Volume
43
Issue
4
Pages
047001–047001
Publication date
17 February 2026
Language
EN