We consider (4, 1)-dimensional branes constructed with two scalar fields $\varphi$ and $\chi$ coupled to a Dirac spinor field by means of a general Yukawa coupling. The equation of motion for the coefficients of the chiral decomposition of the spinor in curved spacetime leads to a Schrödinger-like equation whose solutions allow to obtain the masses of the fermionic modes. The simplest Yukawa coupling $\overline{\Psi }\varphi \chi \Psi$ is considered for the Bloch brane model and fermion localization is studied. We found resonances for both chiralities and related their appearance to branes with internal structure.

We study the gravitation effects on a static and spherically symmetric spacetime due to the vacuum expectation value (VEV) of a Kalb–Ramond field. The Kalb–Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb–Ramond (VEV) and the Ricci tensor, we obtain an exact parameterdependent power-law modified black hole. For a particular choice of the LSB parameter, the Lorentz violation produces a solution similar to the Reissner–Nordstrom, despite the absence of charge. The near-horizon geometry is modified by including a new inner horizon and shifting the Schwarzschild horizon. Asymptotically, the usual Minkowski spacetime with a background tensor field is recovered. The vacuum configurations are studied considering the energy conditions and the Lorentz violating source properties. By means of the mercury perihelion test, an upper bound to the local Lorentz violation (LV) is obtained, and its corresponding effects on the black hole temperature is investigated.

In this work, we investigate the consequences of the spontaneous breaking of Lorentz symmetry, triggered by the bumblebee vector field, on the usual Einstein-Hilbert theory. Specifically, we consider the Einstein-Hilbert action modified by the bumblebee dynamic field, and evaluate the graviton propagator using an extended basis of Barnes-Rivers tensor projectors, involving the Lorentz-violating vector. Once the propagator is carried out, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity. We verify that this model possesses two dispersion relations: one provides causal and unitary propagating modes, while the second one yields a causal but nonunitary mode which spoils the physical consistency of the model.