We have obtained an exact vacuum solution from a gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking, we have investigated some classics tests including the advance of the perihelion, bending of light and Shapiro's time-delay. Furthermore, we have computed some upper-bounds from which the most stringent one attains a sensitivity at the 10 −13 level.

We obtain an exact Kerr like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane rc decreases with the Lorentz breaking constant ℓ > 0, and increases with ℓ < 0.

Abstract:We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F µν F µν . We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or ChernSimons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with |φ| 4 -potential or |φ| 6 -potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

The objective of this case report was to describe the retreatment of an immature upper right central incisor in a 20-year-old female patient after unsuccessful endodontic treatment, who had probable clinical-radiographic diagnosis of a large periapical inflammatory cyst and persistent fistula. After removing the root canal filling material, disinfection of the root canal system, and successive intracanal medication changes over 60 days, the fistula remained active. Therefore, parendodontic surgery was performed. The root canal system was obturated, the periapical cyst was surgically enucleated, and retro-obturation with mineral trioxide aggregate was performed. We used the guided tissue regeneration technique with a xenograft and resorbable membrane. On histopathological examination, we observed bacterial colonies present in the lumen of the cystic lesion. Clinical evaluation, periapical radiograph, and cone-beam tomography confirmed complete healing of the periapical area of the affected tooth. The treatment success was verified by periapical healing over a follow-up period of 21 months.