We show that CPT-even aetherlike Lorentz-breaking actions, for the scalar and electromagnetic fields, are generated via their appropriate Lorentz-breaking coupling to spinor fields, in three, four, and five space-time dimensions. Besides, we also show that aetherlike terms for the spinor field can be generated as a consequence of the same couplings. We discuss the dispersion relations in the theories with aetherlike Lorentz-breaking terms and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the action of the scalar field.

In this work, we calculate the deflection angle of light in a spacetime that interpolates between regular black holes and traversable wormholes, depending on the free parameter of the metric. Afterwards, this angular deflection is substituted into the lens equations which allows us to obtain physically measurable results, such as the position of the relativistic images and the magnifications.

We consider a metric-affine extension to the gravitational sector of the Standard Model extension for the Lorentz-violating coefficients $u$ and $s^{\mu \nu }$. The general results, which are applied to a specific model called metric-affine bumblebee gravity, are obtained. A Schwarzschild-like solution, incorporating effects of the Lorentz symmetry breaking through the coefficient $X=\xi b^2$, is found. Furthermore, a complete study of the geodesic trajectories of particles is accomplished in this background, emphasizing the departure from general relativity. We also compute the advance of Mercury’s perihelion and the deflection of light within the context of the weak-field approximation, and we verify that there exist two new contributions ascribed to the Lorentz symmetry breaking. As a phenomenological application, we compare our theoretical results with observational data in order to estimate the coefficient $X$.

This work deals with braneworld scenarios with generalized gravity. We investigate models where the potential of the scalar field is polynomial or nonpolynomial. We obtain exact and approximated solutions for the scalar field, warp factor and energy density, in the complex scenario with no restriction on the scalar curvature. In particular, we describe the case where the brane may split, engendering internal structure, with the splitting caused by the same parameter that controls deviation from standard gravity

Within the framework of the spontaneous Lorentz symmetry breaking (LSB), we consider a metric-affine generalization of the gravitational sector of the Standard Model Extension (SME), including the Lorentz-violating (LV) coefficients u and s^μν . In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of LSB through the LV dimensionless parameter X = ξb ², with ξ is the nonminimal coupling constant, and b ² = b^μb_μ , with b_μ is the vacuum expectation value of the bumblebee field; as the LSB is turned off, X = 0, we recover the well-established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for X by using astrophysical data of the advance of Mercury's perihelion.