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.
Authors
- Philip K. Schwartz (ORCID: https://orcid.org/0000-0001-7222-9099)
- Domenico Giulini (ORCID: https://orcid.org/0000-0003-3123-7257)
- Arian L. von Blanckenburg (ORCID: https://orcid.org/0009-0008-5430-6319)
Institutions
- Leibniz University Hannover (DE)
- Max Planck Institute for Gravitational Physics (DE)
Publication Details
- Journal
- Classical and Quantum Gravity
- Published
- 2026-02-17
- DOI
- https://doi.org/10.1088/1361-6382/ae4709
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00