https://doi.org/10.1140/epjc/s10052-024-13607-7
Regular Article
Generalized Chern–Pontryagin models
Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraíba, Brazil
Received:
19
July
2024
Accepted:
12
November
2024
Published online:
21
November
2024
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 , i.e.,
. Within this framework, we derive the gravitational field equations and solve them for the particular models,
and
, 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:
, a dynamical degree of freedom, while the second,
, a non-dynamical degree of freedom. In particular, the scalar field
emerges coupled with the Chern–Pontryagin topological term
, i.e.,
, which is nothing more than Chern–Simons term.
© The Author(s) 2024
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