One of the main issues in gravitation is the presence of singularities in the most common space-time solutions of General Relativity, as the case of black holes. A way of constructing regular solutions that remove spacelike singularities consists in implement a bounce on such space-time, leading to what is usually known as black bounce space-times. Such space-times are known to describe regular black holes or traversable wormholes. However, one of the main issues lies on reconstructing the appropriate source that leads to such a solution. In this paper, a reconstruction method is implemented to show that such types of metrics can be well accommodated in non-linear electrodynamics with the presence of a scalar field. Some of the most important black bounces solutions are reconstructed in this framework, both in 3 + 1 as in 2 + 1 dimensions. For the first time in the literature, these solutions have an electrically charged source of matter from non-linear electrodynamics. Specific features are indicated that distinguish electric sources from magnetic ones, previously found for the same space-times.

Two different solutions to the problem of the zero-mode localization of the Elko spinor are presented. The first solution is given by the introduction of a mass term and by coupling the spinor with the brane through a delta function. The second solution is reached by a Yukawa geometrical coupling with the Ricci scalar. These two models consistently change the boundary condition at infinity and at the origin. For the case of the geometrical coupling, we are able to show that the zero mode is localized for any smooth version of the Randall-Sundrum model.

The geometrical localization mechanism in Randall-Sundrum (RS) scenarios is extended by considering the coupling between a quadratic mass term and geometrical tensors. Since the quadratic term is symmetric, tensors with two symmetric indices have to be taken into account. These are the Ricci and the Einstein tensors. For the Ricci tensor, it is shown that a localized zero mode exists while that is not possible for the Einstein tensor. It is already known that the Ricci scalar generates a localized solution but the metrics do not. Therefore, it can be concluded that divergenceless tensors do not localize the zero mode of the gauge fields. The result is valid for any warp factor recovering the RS metrics at the boundaries and, therefore, is valid for RS I and II models. We also compute resonances for all couplings. These are calculated using the transfer matrix method. The cases studied consider the standard RS with deltalike branes and branes generated by kinks and domain walls as well. The parameters are changed to control the thickness of the smooth brane. We find that, for all cases considered, geometrical coupling does not generate resonances. This enforces similar results for the coupling with the Ricci scalar and points to the existence of some unidentified fundamental structure of these couplings.

In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy density and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it.