We study the bending of light in the space-time of black holes in the novel four-dimensional Einstein-Gauss-Bonnet theory of gravity, recently proposed by Glavan and Lin [24]. Using Rindler-Ishak method, the effect of Gauss-Bonnet coupling on the bending angle is studied. We show that a positive Gauss-Bonnet coupling gives a negative contribution to the Schwarzschild-de Sitter deflection angle, as one would expect.

We obtain the static and cylindrically symmetric vacuum solutions of Einstein's field equations in the framework of the brane-world model where the matter is localized on the brane by means of a confining potential. Considering a constant curvature bulk, one interesting solution is studied, which is similar to the cosmic string solution in a de Sitter spacetime which confirms the idea that the extra geometrical terms in the gravitational field equations on the brane may be the origin of a positive cosmological constant which is responsible for the accelerating expansion of the universe. Finally, we investigate the physical properties of this solution.

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