In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension ρ 0 and the charge of black hole ρ q on these parameters and observables.

In this paper we investigate the strong gravitational lansing in a charged squashed Kaluza-Klein Gödel black hole. The deflection angle is considered by the logarithmic term proposed by Bozza et al. Then we study the variation of deflection angle and its parametersā andb . We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole in a Gödel background and by relation between lensing parameters and observables, we estimate the observables for different values of charge, extra dimension and Gödel parameters.

Recently, energy condition inequalities in the context of modified Gauss-Bonnet gravity have been derived in Garcia et al. (Phys. Rev. D, 83:104032, 2011). Using these general inequalities, we examine the viability of specific forms of f (G) models proposed in De Felice and Tsujikawa (Phys. Lett. B, 675:1, 2009) that can be responsible for the late-time cosmic acceleration following the matter era. In doing so we also use the recent estimated values of the deceleration, jerk and snap parameters to obtain the bounds from the weak and strong energy conditions on the parameters of the above mentioned forms of f (G) gravity theories.

In this paper we investigate the strong gravitational lensing in a five dimensional background with Gauss-Bonnet gravity, so that in 4-dimensions the Gauss-Bonnet correction disappears. By considering the logarithmic term for deflection angle, we obtain the deflection angleα and corresponding parametersā andb. Finally, we estimate some properties of relativistic images such as θ ∞ , s and r m .