Matter without matter: Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

We consider Einstein-Gauss-Bonnet gravity in n(≥6)-dimensional Kaluza-Klein spacetime M⁴×K^n-4, where K^n-4 is the Einstein space with negative curvature. In the case where K^n-4 is the space of negative constant curvature, we have recently obtained a new static black-hole solution [Phys. Rev. D 74, 021501(R) (2006)] which is a pure gravitational creation including Maxwell field in four-dimensional vacuum spacetime. The solution has been generalized to make it radially radiate null radiation representing gravitational creation of charged null dust. The same class of solutions though exists in spacetime Mᵈ×K^n-d for $d=3,4$, however the gravitational creation of the Maxwell field is achieved only for $d=4$. Also, the Gauss-Bonnet effect could be brought down to Mᵈ only for $d=4$. Further some new exact solutions are obtained including its analogue in Taub-NUT spacetime on M⁴ for $d=4$.