Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime

Recently, a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory was presented to bypass the Lovelock’s theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $$\alpha \rightarrow \alpha /(D-4)$$ α → α / ( D - 4 ) and to take the limit $$D\rightarrow 4$$ D → 4 . However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem (http://arxiv.org/abs/2003.11552, http://arxiv.org/abs/2003.12771, http://arxiv.org/abs/2004.08362, http://arxiv.org/abs/2004.09472, http://arxiv.org/abs/2004.10716). The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss–Bonnet term in four dimensions contributes to the string geometry in the new theory.

Conformal cylindrically symmetric spacetimes in modified gravity

We investigate cylindrically symmetric spacetimes in the context of [Formula: see text] gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle–Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special [Formula: see text] function convenient to [Formula: see text]-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different [Formula: see text] models. Finally, geometrical and physical results of the solutions are discussed.

KINKS, ENERGY CONDITIONS AND CLOSED TIMELIKE CURVES

A link between the possibility of extending a geodesically incomplete kinked spacetime to a spacetime which is geodesically complete and the energy conditions is discussed for the case of a cylindrically-symmetric spacetime kink. It is concluded that neither the strong nor the weak energy condition can be satisfied in the four-dimensional example, though the latter condition may survive on the transversal sections of such a spacetime. It is also shown that the matter which propagates quantum-mechanically in a kinked spacetime can always be trapped by closed timelike curves, but signaling connections between that matter and any possible observer can only be made of totally incoherent radiation, so preventing observation of causality violation.