The trace-free Einstein tensor is not variational for the metric as field variable
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915822548549632 |
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| author | von Blanckenburg, Arian L. Giulini, Domenico Schwartz, Philip K. |
| author_facet | von Blanckenburg, Arian L. Giulini, Domenico Schwartz, Philip K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The trace-free Einstein tensor is not variational for the metric as field variable von Blanckenburg, Arian L. Giulini, Domenico Schwartz, Philip K. General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Analysis of PDEs 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. |
| title | The trace-free Einstein tensor is not variational for the metric as field variable |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2509.02490 |