Generalized Chern–Pontryagin models
Abstract 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 $$ ^*RR$$ ∗ R R , i.e., $$f(R, ^*RR)$$ f ( R , ∗ R R ) ....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-11-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-13607-7 |
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| author | J. R. Nascimento A. Yu. Petrov P. J. Porfírio Ramires N. da Silva |
| author_facet | J. R. Nascimento A. Yu. Petrov P. J. Porfírio Ramires N. da Silva |
| author_sort | J. R. Nascimento |
| collection | DOAJ |
| description | Abstract 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 $$ ^*RR$$ ∗ R R , i.e., $$f(R, ^*RR)$$ f ( R , ∗ R R ) . Within this framework, we derive the gravitational field equations and solve them for the particular models, $$f(R, ^*RR)=R+\beta ( ^*RR)^2$$ f ( R , ∗ R R ) = R + β ( ∗ R R ) 2 and $$f(R, ^*RR)=R+\alpha R^2+\beta ( ^*RR)^2$$ f ( R , ∗ R R ) = R + α R 2 + β ( ∗ R R ) 2 , considering two ansatzes: the slowly rotating Schwarzschild 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, for specific sort of perturbed metric functions. 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: $$\Phi $$ Φ , a dynamical degree of freedom, while the second, $$\vartheta $$ ϑ , a non-dynamical degree of freedom. In particular, the scalar field $$\vartheta $$ ϑ emerges coupled with the Chern–Pontryagin topological term $$ ^*RR$$ ∗ R R , i.e., $$\vartheta ^*RR$$ ϑ ∗ R R , which is nothing more than Chern–Simons term. |
| format | Article |
| id | doaj-art-788e0dce83334f1f8eb3fe3a14a9b68b |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-788e0dce83334f1f8eb3fe3a14a9b68b2024-12-29T12:44:07ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-11-01841111110.1140/epjc/s10052-024-13607-7Generalized Chern–Pontryagin modelsJ. R. Nascimento0A. Yu. Petrov1P. J. Porfírio2Ramires N. da Silva3Departamento de Física, Universidade Federal da ParaíbaDepartamento de Física, Universidade Federal da ParaíbaDepartamento de Física, Universidade Federal da ParaíbaDepartamento de Física, Universidade Federal da ParaíbaAbstract 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 $$ ^*RR$$ ∗ R R , i.e., $$f(R, ^*RR)$$ f ( R , ∗ R R ) . Within this framework, we derive the gravitational field equations and solve them for the particular models, $$f(R, ^*RR)=R+\beta ( ^*RR)^2$$ f ( R , ∗ R R ) = R + β ( ∗ R R ) 2 and $$f(R, ^*RR)=R+\alpha R^2+\beta ( ^*RR)^2$$ f ( R , ∗ R R ) = R + α R 2 + β ( ∗ R R ) 2 , considering two ansatzes: the slowly rotating Schwarzschild 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, for specific sort of perturbed metric functions. 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: $$\Phi $$ Φ , a dynamical degree of freedom, while the second, $$\vartheta $$ ϑ , a non-dynamical degree of freedom. In particular, the scalar field $$\vartheta $$ ϑ emerges coupled with the Chern–Pontryagin topological term $$ ^*RR$$ ∗ R R , i.e., $$\vartheta ^*RR$$ ϑ ∗ R R , which is nothing more than Chern–Simons term.https://doi.org/10.1140/epjc/s10052-024-13607-7 |
| spellingShingle | J. R. Nascimento A. Yu. Petrov P. J. Porfírio Ramires N. da Silva Generalized Chern–Pontryagin models European Physical Journal C: Particles and Fields |
| title | Generalized Chern–Pontryagin models |
| title_full | Generalized Chern–Pontryagin models |
| title_fullStr | Generalized Chern–Pontryagin models |
| title_full_unstemmed | Generalized Chern–Pontryagin models |
| title_short | Generalized Chern–Pontryagin models |
| title_sort | generalized chern pontryagin models |
| url | https://doi.org/10.1140/epjc/s10052-024-13607-7 |
| work_keys_str_mv | AT jrnascimento generalizedchernpontryaginmodels AT ayupetrov generalizedchernpontryaginmodels AT pjporfirio generalizedchernpontryaginmodels AT ramiresndasilva generalizedchernpontryaginmodels |