Generalized Chern-Pontryagin models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910706498011136 |
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| author | Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. da Silva, Ramires N. |
| author_facet | Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. da Silva, Ramires N. |
| contents | We formulate a new class of modified gravity models, that is, generalized four-dimensional Chern-Pontryagin models, whose action is characterized by an arbitrary function of the Ricci scalar $R$ and the Chern-Pontryagin topological term ${}^*RR$, i.e., $f(R, {}^*RR)$. Within this framework, we derive the gravitational field equations and solve them for a particular model, $f(R, {}^*RR)=R+β({}^*RR)^2$, considering two ansatzes: the slowly rotating metric and first-order perturbations of Gödel-type metrics. For the former, we find a first-order correction to the frame-dragging effect boosted by the parameter $L$, which characterizes the departures from general relativity results. For the latter, Gödel-type metrics hold unperturbed. We conclude this paper by displaying that generalized four-dimensional Chern-Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: $Φ$, a dynamical degree of freedom, while the second, $\vartheta$, a non-dynamical degree of freedom. In particular, the scalar field $\vartheta$ emerges coupled with the Chern-Pontryagin topological term ${}^*RR$, i.e., $\vartheta {}^*RR$, which is nothing more than Chern-Simons term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Chern-Pontryagin models Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. da Silva, Ramires N. General Relativity and Quantum Cosmology High Energy Physics - Theory We formulate a new class of modified gravity models, that is, generalized four-dimensional Chern-Pontryagin models, whose action is characterized by an arbitrary function of the Ricci scalar $R$ and the Chern-Pontryagin topological term ${}^*RR$, i.e., $f(R, {}^*RR)$. Within this framework, we derive the gravitational field equations and solve them for a particular model, $f(R, {}^*RR)=R+β({}^*RR)^2$, considering two ansatzes: the slowly rotating metric and first-order perturbations of Gödel-type metrics. For the former, we find a first-order correction to the frame-dragging effect boosted by the parameter $L$, which characterizes the departures from general relativity results. For the latter, Gödel-type metrics hold unperturbed. We conclude this paper by displaying that generalized four-dimensional Chern-Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: $Φ$, a dynamical degree of freedom, while the second, $\vartheta$, a non-dynamical degree of freedom. In particular, the scalar field $\vartheta$ emerges coupled with the Chern-Pontryagin topological term ${}^*RR$, i.e., $\vartheta {}^*RR$, which is nothing more than Chern-Simons term. |
| title | Generalized Chern-Pontryagin models |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.01453 |