Note on the matter coupling in Exotic General Massive 3D Gravity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914247360905216 |
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| author | Cebeci, Hakan |
| author_facet | Cebeci, Hakan |
| contents | In this work, within exterior algebra formalism, we revisit and study the matter coupling in Exotic General Massive 3D Gravity (EGMG), previously introduced in \cite{ozkan_1}. Considering that the matter Lagrangian is both metric co-frame and connection dependent in general, we explicitly construct associated source 2-form by algebraically solving auxiliary 1-form fields in terms of gravitational field variables, energy-momentum and hyper-momentum 2-forms. It is seen that that the source 2-form involves terms that are quadratic in energy-momentum and hyper-momentum 2-forms as well as terms that depend on covariant derivatives of them. In addition, we derive the consistency relation in order that matter-coupled EGMG field equation be third-way consistent. In general, the consistency requires a particular relation that should be satisfied by energy-momentum and hyper-momentum 2-forms. We note that our construction and formalism allows to investigate non-minimal matter couplings with gravitational fields. It also enables to construct the higher order curvature extensions of EGMG. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_06908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note on the matter coupling in Exotic General Massive 3D Gravity Cebeci, Hakan General Relativity and Quantum Cosmology High Energy Physics - Theory In this work, within exterior algebra formalism, we revisit and study the matter coupling in Exotic General Massive 3D Gravity (EGMG), previously introduced in \cite{ozkan_1}. Considering that the matter Lagrangian is both metric co-frame and connection dependent in general, we explicitly construct associated source 2-form by algebraically solving auxiliary 1-form fields in terms of gravitational field variables, energy-momentum and hyper-momentum 2-forms. It is seen that that the source 2-form involves terms that are quadratic in energy-momentum and hyper-momentum 2-forms as well as terms that depend on covariant derivatives of them. In addition, we derive the consistency relation in order that matter-coupled EGMG field equation be third-way consistent. In general, the consistency requires a particular relation that should be satisfied by energy-momentum and hyper-momentum 2-forms. We note that our construction and formalism allows to investigate non-minimal matter couplings with gravitational fields. It also enables to construct the higher order curvature extensions of EGMG. |
| title | Note on the matter coupling in Exotic General Massive 3D Gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.06908 |