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We study the greybody factors, quasinormal modes, and shadow of the higher dimensional de-Sitter (dS)/anti de-Sitter (AdS) black hole spacetimes derived from the Einstein-bumblebee gravity theory within the Lorentz symmetry breaking (LSB) framework. We specifically apply the semi-analytical WKB method and the time domain approach to study the scalar and Dirac perturbations of the black hole. In-depth researches are done on the effects of the LSB and dimensionality on the bosonic/fermionic greybody factors, quasinormal modes, and shadow of the higher dimensional bumblebee black hole. The results obtained are discussed, tabulated, and illustrated graphically. [ABSTRACT FROM AUTHOR]

By assuming the cosmological principle i.e., an isotropic and homogeneous universe, we consider the cosmology of a vector-tensor theory of gravitation known as the bumblebee model. In this model a single Lorentz-violating timelike vector field with a nonzero vacuum expectation value (VEV) couples to the Ricci tensor and scalar, as well. Taking the ansatz B (t) ∼ t β for the time evolution of the vector field, where β is a free parameter, we derive the relevant dynamic equations of the Universe. In particular, by employing observational data coming from the Big Bang Nucleosynthesis (BBN) and the matter–antimatter asymmetry in the baryogenesis era, we impose some constraints on the VEV of the bumblebee timelike vector field i.e., ξ b 2 , and the exponent parameter β . The former and the latter limit the size of Lorentz violation, and the rate of the time evolution of the background Lorentz-violating bumblebee field, respectively. [ABSTRACT FROM AUTHOR]

We have studied the quasinormal modes (QNMs) of a slowly rotating black hole with Lorentz-violating parameter in Einstein–Bumblebee gravity. We analyse the slow rotation approximation of the rotating black hole in the Einstein–Bumblebee gravity, and obtain the master equations for scalar perturbation, vector perturbation and axial gravitational perturbation, respectively. Using the matrix method and the continuous fraction method, we numerically calculate the QNM frequencies. In particular, for scalar field, it shows that the QNMs up to the second order of rotation parameter have higher accuracy. The numerical results show that, for both scalar and vector fields, the Lorentz-violating parameter has a significant effect on the imaginary part of the QNM frequencies, while having a relatively smaller impact on the real part of the QNM frequencies. But for axial gravitational perturbation, the effect of increasing the Lorentz-violating parameter ℓ is similar to that of increasing the rotation parameter a ~ . [ABSTRACT FROM AUTHOR]

Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR spectrum of the Galactic black hole EXO 1846-031 in order to constrain the Lorentz-violating parameter ℓ . We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter ℓ because of a very strong degeneracy between the estimates of ℓ and of the black hole spin parameter a ∗ . Such a degeneracy may be broken by combining other observations. [ABSTRACT FROM AUTHOR]

We consider a bumblebee gravity-based Kerr-like black hole in a noncommutative (NC) background and study the superradiance effect and the shadow cast. We extensively study the different aspects of the black hole associated with a generalized Kerr-like spacetime metric endowed with the corrections jointly linked with Lorentz violation and NC spacetime effect. We examine the deviation of shape, and size of the ergosphere, energy emission rate, in this generalized situation. We also examine the influence of admissible values of Lorentz violating parameter ℓ and NC parameter b on the superradiance effect and shadow of the black hole. The admissible range has been determined from the observation of the Event Horizon Telescope (EHT) collaboration concerning M 87 ∗ astronomical black hole. We observe that the superradiance phenomena has a crucial dependence on the parameter ℓ and b apart from its dependence on a or a ^ = ℓ + 1 a which is linked with the spin of the black hole. We also observe that with the increase in Lorentz violating parameter ℓ , the size of the black hole shadow increases, and with the increase in the NC parameter b the size of the black hole decreases. We have made an attempt to constrain the NC parameters b of this modified Kerr-like black hole by using the data available from the Event Horizon Telescope (EHT) collaboration. This study shows that black holes associated with NC Kerr-like spacetime may be a suitable candidate for the astrophysical black holes. [ABSTRACT FROM AUTHOR]

This work belongs to the context of the standard-model extension, in which a Lorentz symmetry violation is induced by a bumblebee field as it acquires a nonzero vacuum expectation value. The mathematical formulation of a generic bumblebee model and its associated dynamical equations are presented. Then, these equations are considered for the vacuum and a substantial simplification is performed for the particular case of a gradient bumblebee field at its vacuum expectation value. After some further manipulation, a method to easily find solutions to the model is developed, in which the exact effect on the spacetime description due to the presence of this bumblebee field is explicitly provided. As some examples, the method is applied to determine the implications of the bumblebee field on the Schwarzschild spacetime and also on a rotating one. A previously published solution is recovered and some new ones are obtained. In the rotating situation, a simple solution is found which contains both the Kerr solution and the already published one as special cases. It is also shown its distinguished surfaces are still given by the same corresponding expressions for the Kerr solution. In conclusion, the mathematical improvement made is considered to be a significant contribution to the theory as a powerful tool to investigate its many aspects and consequences. [ABSTRACT FROM AUTHOR]

Someone else like us can check that the equations of motion for the bumblebee field (with HT ht ): 4 HT ht Graph can not be satisfied with metric (1) and the following bumblebee field given in [[2]] 5 HT ht Graph which yields HT ht where I C i is a positive constant. [Extracted from the article]

We have considered the bumblebee gravity model where lorentz-violating (LV) scenario gets involved through a bumblebee field vector field B μ . A spontaneous symmetry breaking allows the field to acquires a vacuum expectation value that generates LV into the system. A Kerr–Sen-like solution has been found out starting from the generalized form of a radiating stationery axially symmetric black hole metric. We compute the effective potential offered by the null geodesics in the bumblebee rotating black hole spacetime. The shadow has been sketched for different variations of the parameters involved in the system. A careful investigation has been carried out to study how the shadow gets affected when Lorentz violation enters into the picture. The emission rate of radiation has also been studied and how it varies with the LV parameter ℓ is studied scrupulously. [ABSTRACT FROM AUTHOR]

We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the post-Minkowskian, weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory. [ABSTRACT FROM AUTHOR]

It is shown that the paper "Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model" (Kanzi and Sakallı in Eur Phys J C 81:501, 2021) recently published in this journal is based on an incorrect result obtained by Ding et al. (Eur Phys J C 80:178, 2020) for a Kerr-like black hole solution. [ABSTRACT FROM AUTHOR]