Metric symmetry by design in general relativity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912515411148800 |
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| author | Toth, Viktor T. |
| author_facet | Toth, Viktor T. |
| contents | The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's attempted Unified Field Theory or Moffat's Nonsymmetric Gravitational Theory. Explicitly enforcing the constraint by means of a Lagrange-multiplier term restores Einstein's field equations, but the multiplier appears as an additional, unconstrained antisymmetric term. We briefly discuss the possible significance of this term with respect to a nonvanishing cosmological angular momentum, a sourced spin current, the nonsymmetric nature of the Einstein pseudotensor characterizing the energy-momentum of the gravitational field, and possible implications on attempts to obtain a quantum theory of gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metric symmetry by design in general relativity Toth, Viktor T. General Relativity and Quantum Cosmology The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's attempted Unified Field Theory or Moffat's Nonsymmetric Gravitational Theory. Explicitly enforcing the constraint by means of a Lagrange-multiplier term restores Einstein's field equations, but the multiplier appears as an additional, unconstrained antisymmetric term. We briefly discuss the possible significance of this term with respect to a nonvanishing cosmological angular momentum, a sourced spin current, the nonsymmetric nature of the Einstein pseudotensor characterizing the energy-momentum of the gravitational field, and possible implications on attempts to obtain a quantum theory of gravity. |
| title | Metric symmetry by design in general relativity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.10607 |