In this work, we investigate the influence of the Lorentz symmetry breaking in the gravitational bending angle for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a nonzero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances and it is applicable to non asymptotically flat spacetimes when considering the receiver viewpoint. We also study the bending angle of massive particles, where we systematize the Ishihara method for its application in Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider three backgrounds. Two of them are asymptotically flat and were found by Bertolamy et al and Casana et al. The third was found very recently by Maluf et al and is not asymptotically flat due to an effective cosmological constant.I.

This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.

In this paper, we investigate the gravitational bending angle due to the Casimir wormholes, which consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP) corrections of Casimir energy. We use the Ishihara method for the Jacobi metric, which allows us to study the bending angle of light and massive test particles for finite distances. Beyond the uncorrected Casimir source, we consider many GUP corrections, namely, the Kempf, Mangano and Mann (KMM) model, the Detournay, Gabriel and Spindel (DGS) model, and the so-called type II model for the GUP principle. We also find the deflection angle of light and massive particles in the case of the receiver and the source are far away from the lens. In this case, we also compute the optical scalars: convergence and shear for these Casimir wormholes as a gravitational weak lens. Our self-consistent iterative calculations indicate corrections to the bending angle by Casimir wormholes in the previous paper.

In this paper, we study the scalar (tensor) and vector unparticle corrections for cosmic and black strings. Initially, we consider a static cosmic string ansatz from which we obtain the solution in terms of first- and second-kind Bessel functions. We also obtain the solution for a black string in the unparticle scenario. We identify two regimes, namely, a gravity-dominated regime and an ungravity-dominated regime. In the gravity-dominated regime, the black string solution recovers the usual solution for black strings. The Hawking temperature is also studied in both regimes. As in the static and rotating black hole, we find a fractalization of the event horizon. This points to the fact that fractalization is a natural consequence of unparticles. Finally, we study the thermodynamics of the black string in the ungravity scenario by computing the entropy, heat capacity, and free energy. For both cases, we find that, depending on the region of the parameter $$d_U$$ d U , phase transitions are possible.

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