Bumblebee Gravity Research Articles

Black holes with a cosmological constant in bumblebee gravity

In this work, we present black hole solutions with a cosmological constant in bumblebee gravity, which provides a mechanism for the Lorentz symmetry violation by assuming a nonzero vacuum expectation value for the bumblebee field. From the gravitational point of view, such solutions are spherically symmetric black holes with an effective cosmological constant and are supported by an anisotropic energy-momentum tensor, conceived of as the manifestation of the bumblebee field in the spacetime geometry. Then we calculate the shadow angular radius for the proposed black hole solution with a positive effective cosmological constant. In particular, our results are the very first relation between the bumblebee field and the shadow angular size.

Relative time delay in Bumblebee gravity

We study the effect of the Bumblebee deviation parameter $l$ on galactic scale by means of Relative Time Delay (RTD) caused by frame dragging effect. While weak field solar system tests have been fairly accurately measured leading to an exceedingly tiny upper limit $l\leq10^{-13}$ , measurements on the large astrophysical scale are yet unavailable, so we decided to keep $l$ neither too tiny nor too large. The present work demonstrates a method of calculating the RTD as a diagnostic that could be profitably used in many other situations as well.

Circular orbit of a particle and weak gravitational lensing

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

Finite-distance gravitational deflection of massive particles by a Kerr-like black hole in the bumblebee gravity model

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. In particular, we correct a mistake in the previous literature. Furthermore, we consider the finite-distance correction for the deflection angle of massive particles.

GUP modified Hawking radiation in bumblebee gravity

The effect of Lorentz symmetry breaking (LSB) on the Hawking radiation of Schwarzschild-like black hole found in the bumblebee gravity model (SBHBGM) is studied in the framework of quantum gravity. To this end, we consider Hawking radiation spin-0 (bosons) and spin-12 particles (fermions), which go in and out through the event horizon of the SBHBGM. We use the modified Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and LSB. In particular, we reveal that, independent of the spin of the emitted particle, GUP causes a change in the Hawking temperature of the SBHBGM. Furthermore, we compute the semi-analytic greybody factors (for both bosons and fermions) of the SBHBGM. Thus, we reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor. Our findings are graphically depicted.

Ricci dark energy in bumblebee gravity model

The Ricci dark energy is a model inspired by the holographic dark energy models with the dark energy density being proportional to Ricci scalar curvature. Here, this model is studied in the bumblebee gravity theory. It is a gravitational theory that exhibit spontaneous Lorentz symmetry breaking. Then, the modified Friedmann equation is solved for two cases. In the first case, the coupling constant [Formula: see text] is equal to zero and in the second case a solution in the vacuum, where the bumblebee field becomes a constant that minimizes the potential, is considered. The coupling constant controls the interaction gravity-bumblebee.

Quasinormal modes of bumblebee wormhole

In this work, we calculate the quasinormal frequencies from a bumblebee traversable wormhole. The bumblebee wormhole model is based on the bumblebee gravity, which exhibits a spontaneous Lorentz symmetry breaking. Supporting by the Lorentz violation parameter , this model allows for the fulfillment of the flare-out and energy conditions, granted non-exotic matter to the wormhole. We analyze the parameters of the bumblebee wormhole in order to obtain a Regge–Wheeler’s equation with a bell-shaped potential. We obtain the quasinormal modes (QNMs) via the WKB approximation method for both scalar and gravitational perturbations. The time domain has decreasing oscillation (damping) profiles for the bumblebee wormhole.

Exact traversable wormhole solution in bumblebee gravity

In this study, we found a new traversable wormhole solution in the framework of a bumblebee gravity model. With these types of models, the Lorentz symmetry violation arises from the dynamics of a bumblebee vector field that is non-minimally coupled with gravity. To this end, we checked the wormhole's flare-out and energy (null, weak, and strong) conditions. We then studied the deflection angle of light in the weak limit approximation using the Gibbons-Werner method. In particular, we show that the bumblebee gravity effect leads to a non-trivial global topology of the wormhole spacetime. By using the Gauss-Bonnet theorem (GBT), it is shown that the obtained non-asymptotically flat wormhole solution yields a topological term in the deflection angle of light. This term is proportional to the coupling constant, but independent from the impact factor parameter. Significantly, we showed that the bumblebee wormhole solutions, under specific conditions, support the normal matter wormhole geometries.

Gravitational lensing under the effect of Weyl and bumblebee gravities: Applications of Gauss–Bonnet theorem

In this paper, we use the Gauss–Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss–Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as compared with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee gravity. Moreover, we investigate the deflection angle by Einstein–Rosen type wormhole in Weyl gravity and in bumblebee gravity. Interestingly, the deflection angle by Einstein–Rosen type wormhole in bumblebee gravity is found as larger than the deflection angle by Einstein–Rosen type wormhole in Weyl gravity.

Exact Schwarzschild-like solution in a bumblebee gravity model

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.

Gödel solution in the bumblebee gravity

Here, we consider a gravity theory involving a spontaneous Lorentz symmetry breaking called the bumblebee model. We show that, at certain values of the bumblebee field, the Gödel metric is consistent within this theory.