Bumblebee Field Research Articles

An exact stationary axisymmetric vacuum solution within a metric-affine bumblebee 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 sμν . 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 = bμbμ , with bμ 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.

Violation of Hod’s conjecture and probing it with optical properties of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity

In this work, the quasinormal modes of a 5-D black hole in Einstein Gauss–Bonnet Bumblebee theory of gravity have been investigated with the help of the Padé averaged higher order WKB approximation method and the validity of Hod’s conjecture has been studied. It is found that the presence of Lorentz symmetry breaking due to the Bumblebee field favours Hod’s conjecture. But in the case of the Gauss–Bonnet term, an increase in the coupling parameter increases the chances of violation of Hod’s conjecture. We further investigated the optical properties of the black hole viz., shadow and emission rate. It is found that a black hole with a lower lifetime favours Hod’s conjecture.

Notes on thermodynamics of Schwarzschild-like bumblebee black hole

In this work, we revisited the thermodynamics of Schwarzschild-like bumblebee black hole using Iyer–Wald covariant phase space formalism. With a non zero vacuum expectation value, the bumblebee field is responsible for spontaneously breaking the Lorentz symmetry. As the bumblebee field is non-minimally coupled to gravity, we showed that the thermodynamic variables will be different from the counterpart in Einstein gravity. Especially, by using Iyer–Wald formalism, we found that the black hole entropy also differs from the result obtained from Wald entropy formula. Like Horndeski gravity, this mismatch is due to the divergence of bumblebee one-form field at the horizon. After figuring out the thermodynamics, we also briefly discussed the evaporation behavior of Schwarzschild like bumblebee black hole. We found that although bumblebee field has no influence on the critical impact factor, it can influence the black hole evaporation time.

Probing Schwarzschild-like black holes in metric-affine bumblebee gravity with accretion disk, deflection angle, greybody bounds, and neutrino propagation

In this paper, we investigate Schwarzschild-like black holes within the framework of metric-affine bumblebee gravity. We explore the implications of such a gravitational setup on various astrophysical phenomena, including the presence of an accretion disk, the deflection angle of light rays, the establishment of greybody bounds, and the propagation of neutrinos. The metric-affine bumblebee gravity theory offers a unique perspective on gravitational interactions by introducing a vector field that couples to spacetime curvature. We analyze the behavior of accretion disks around Schwarzschild-like black holes in this modified gravity scenario, considering the effects of the bumblebee field on the accretion process. Furthermore, we scrutinize the deflection angle of light rays as they traverse the gravitational field, highlighting potential deviations from standard predictions due to the underlying metric-affine structure. Investigating greybody bounds in this context sheds light on the thermal radiation emitted by black holes and how the modified gravity framework influences this phenomenon. Moreover, we explore neutrino propagation around Schwarzschild-like black holes within metric-affine bumblebee gravity, examining alterations in neutrino trajectories and interactions compared to conventional general relativity. By comprehensively probing these aspects, we aim to unravel the distinctive features and consequences of Schwarzschild-like black holes in the context of metric-affine bumblebee gravity, offering new insights into the nature of gravitational interactions and their observable signatures.

Braneworlds in bumblebee gravity

We investigate thick-brane solutions within the five-dimensional bumblebee gravity in the presence of a real scalar field. Specifically, we implement the Lorentz symmetry breaking scenario within this context and obtain brane-like structures. Since the contribution of the bumblebee field is expected to be weak, we solve the field equations in the small-parameter regime. In this situation, we develop a first-order framework to describe the brane. The results show that the function which drives the bumblebee field may engender a lumplike structure whose shape depends on the parameters. On one hand, the effect of the non-minimal coupling, controlled by ξ, between the bumblebee field and gravity shifts the field from the vacuum expectation value. On the other hand, the aether parameter, β, is responsible for modifying the solution inside the brane.

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations and the bumblebee motion equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating and can only exist with a linear functional potential of the bumblebee field. This black hole has two horizons and an ergosphere which are dependent on the bumblebee coupling constant ell . The concepts of the area and volume of the horizon should be renewed in this LV spacetime due to the nontrivial contribution of coupling between the bumblebee field and the Ricci tensor. Only in this way, the entropy-area relation, first law of thermodynamics and the Smarr formula can still be constructed. We also study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

Constraining the Lorentz-violating bumblebee vector field with big bang nucleosynthesis and gravitational baryogenesis

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)sim t^beta for the time evolution of the vector field, where beta 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., xi b^2, and the exponent parameter beta . 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.

Spontaneous Lorentz symmetry breaking effects on GRBs jets arising from neutrino pair annihilation process near a black hole

The study of neutrino pair annihilation into electron-positron pairs (nu {bar{nu }}rightarrow e^-e^+) is astrophysically well-motivated because it is a possible powering mechanism for the gamma-ray bursts (GRBs). In this paper, we estimate the gamma-ray energy deposition rate (EDR) arising from the annihilation of the neutrino pairs in the equatorial plane of a slowly rotating black hole geometry modified by the broken Lorentz symmetry (induced by a background bumblebee vector field). More specifically, owing to the presence of a dimensionless Lorentz symmetry breaking (LSB) parameter l arising from nonminimal coupling between the bumblebee field with nonzero vacuum expectation value and gravity, the metric solution in question differs from the standard slowly rotating Kerr black hole. By idealizing the thin accretion disk temperature profile in the two forms of isothermal and gradient around the bumblebee gravity-based slow rotating black hole, we investigate the influence of spontaneous LSB on the nu {bar{nu }}-annihilation efficiency. For both profiles, we find that positive values of LSB parameter l>0 induce an enhancement of the EDR associated with the neutrino-antineutrino annihilation. Therefore, the process of powering the GRBs jets around bumblebee gravity modified slowly rotating geometry is more efficient in comparison with standard metric. Using the observed gamma-ray luminosity associated with different GRBs types (short, long, and ultra-long), we find, through the analysis of the EDR in the parameter space l-a (a^2ll 1), some allowed ranges for the LSB parameter l.

The bumblebee field excitations in a cosmological braneworld

We investigate the effects of the spacetime curvature and extra dimensions on the excitations of the Lorentz violating bumblebee field B μ . By assuming the bumblebee field living in a five-dimensional AdS 5 bulk, we found an exponential suppression of the bumblebee self-interacting constant λ and of the bumblebee vacuum expectation value (VEV) b M along the fifth extra dimension. The fluctuations of the bumblebee field upon the VEV can be decomposed into transverse and longitudinal modes with respect to b M . For a spacelike b M along the extra dimension and assuming a thin FRW 3-brane embedded in the AdS 5, the transverse mode is localized on the brane. The bulk geometry leads to a propagating and unbound longitudinal mode along the extra dimension. On the brane, the cosmological expansion leads to the decay of the longitudinal mode in time, as Δt ≈ H −1.

High dimensional AdS-like black hole and phase transition in Einstein-bumblebee gravity* *Supported by the Scientific Research Fund of the Hunan Provincial Education Department (19A257 and 19A260), the National Natural Science Foundation (NNSFC) of China (11247013), Hunan Provincial Natural Science Foundation of China (2015JJ2085)

In this study, we obtained an exact high dimensional anti-de Sitter (AdS) black hole solution in Einstein-bumblebee gravity theory. This AdS-like black hole can only exist with a linear functional potential of the bumblebee field. We found that the Smarr formula and the first law of black hole thermodynamics can still be constructed in this Lorentz symmetry breaking black hole spacetime, but the conceptions of the black hole horizon area/entropy and the volume inside the horizon should be renewed due to its anisotropy. We also found that two types of phase transition exist: small-large black hole phase transition and Hawking-Page phase transition, like those of the Schwarzschild AdS black hole. After Lorentz symmetry breaking, the black hole mass at the divergent point of heat capacity becomes small, and the Gibbs free energy of the meta-stable large black hole is also smaller, showing that the large stable black hole can be more easily formed.

Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

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.

Kerr–Sen-like Lorentz violating black holes and superradiance phenomena

A Kerr–Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr–Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated with it. We observe that for the low-frequency range of the scalar wave the superradiance scattering gets enhanced when the Lorentz-violating parameter ell takes the negative values and it reduces when values of ell are positive. The study of the black hole bomb issue reveals that for the negative values of ell , the parameter space of the scalar field instability increase prominently, however, for its positive values, it shows a considerable reduction. We also tried to put constraints on the parameters contained in the Kerr–Sen-like black hole by comparing the deformation of the shadow produced by the black hole parameters with the observed deviation from circularity and the angular deviation from the M87* data.

Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime

We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector. We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme. We also obtain a Schwarzschild-like bumblebee black hole solution in D-dimensional spacetime. We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential. That is, its gravitational potential has a minimum value (negative) in the black hole interior and has a positive value 1+ℓ at short distance r→0. If the constant ℓ is large enough, then this kind of black hole is practically free from the singularity problem. The thermodynamics and phase transition are also studied. In a cosmological context, it is interesting that the Gauss-Bonnet term has no effect on the conservation of energy equation. A late-time expansion of de Sitter universe can be replicated in an empty space. The Gauss-Bonnet term and the bumblebee field can both actually act as a form of dark energy.

Radiative corrections in metric-affine bumblebee model

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 weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric which, besides the zeroth-order Minkowskian contribution, also has the vector field contributions of the bumblebee, and show that it is renormalizable at one-loop level. From our analysis it also follows that the non-metricity of this theory is determined by the gradient of the bumblebee field, and that it can acquire a vacuum expectation value due to the contribution of the bumblebee field.

Magnetic reconnection and energy extraction from a spinning black hole with broken Lorentz symmetry

In the Penrose process and the Blandford-Znajek mechanism, the rotational energy of a black hole (BH) is extracted via particle fission and magnetic tension, respectively. Recently, inspired by a fundamental trait in plasma astrophysics known as magnetic reconnection (MR), a new energy extraction mechanism based on the fast reconnection of the magnetic field lines inside the ergosphere has been proposed by Comisso and Asenjo. In this paper, we investigate energy extraction caused by MR in the ergosphere of a rapidly spinning BH with broken Lorentz symmetry by a background bumblebee vector field. The desired rotating BH solution differentiates from the standard Kerr BH via the Lorentz symmetry breaking (LSB) parameter $l$, which comes from nonminimal coupling between the bumblebee field with nonzero vacuum expectation value and gravity. We find that incorporating $l<0$ in the background is in the interest of the energy extraction via MR for the fast-spinning BH surrounded by the plasma with weak magnetization, below what is expected from the scenario by Comisso and Asenjo. Our analysis robustly indicates that the power of energy extraction and efficiency of the plasma energization process through fast MR is more efficient than the Comisso-Asenjo solution, provided that the LSB parameter is negative, $l<0$. Compared to the Blandford-Znajek mechanism arising from the underlying background, we also show that MR is a more efficient energy extraction mechanism if $l<0$.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

Bumblebee field as a source of cosmological anisotropies

In this work, a bumblebee field is adopted in order to generate cosmological anisotropies. For that purpose, weassume a Bianchi I cosmology, as the background geometry, and a bumblebee field coupled to it.Bumblebee models are examples of a mechanism for the Lorentz symmetry violation byassuming a nonzero vacuum expectation value for the bumblebee field. When coupled tothe Bianchi I geometry, which is not in agreement with a cosmological principle, the bumblebee fieldplays the role of a source of anisotropies and produces a preferred axis. Thus, a fraction of the cosmic anisotropieswould come from the Lorentz symmetry violation.In the last part of the article, we try to assume an upper bound on the bumblebee field usingthe quadrupole and octopole moments of the cosmic microwave background radiation.

The gravitational bending angle by static and spherically symmetric black holes in bumblebee gravity

This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.

Metric-affine bumblebee gravity: classical aspects

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.

Bumblebee gravity with a Kerr\u2013Sen like solution and its Shadow

We have considered the bumblebee gravity model where lorentz-violating (LV) scenario gets involved through a bumblebee field vector field B_mu . 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 ell is studied scrupulously.