Lorentz-violating Parameters Research Articles

Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity

In this paper, we study the scenario in which the matter field is an electromagnetic field nonminimally coupled to the bumblebee vector field. We present exact charged spherically symmetric black hole solutions and slowly rotating charged solutions in bumblebee gravity with and without a cosmological constant. The static spherically symmetric solutions describe the Reissner–Nordström-like black hole and Reissner–Nordström-(anti) de Sitter-like black hole, while the stationary and axially symmetric solutions describe the Kerr–Newman-like black hole and Kerr–Newman–(anti) de Sitter-like black hole. We utilize the Hamilton–Jacobi formalism to study the shadows of the black holes. Additionally, we investigate the effect of the electric charge and Lorentz-violating parameters on the radius of the shadow reference circle and the distortion parameter. We find that the radius of the reference circle decreases with the Lorentz-violating parameter and the charge parameter, while the distortion parameter increases with the Lorentz-violating parameter and the charge parameter.

Phase structure and optical properties of the de Sitter Spacetime with KR field based on the Lyapunov exponent

Since the spontaneously broken of the Lorentz symmetry in the gravity theory with the non-minimally coupling between the Kalb–Ramond (KR) field (that acquires a nonzero vacuum expectation value) and the Einstein gravity, there exists the exactly static and spherically symmetric black holes solutions related with the Lorentz violating parameter. Based on this, we consider the corresponding black hole solution in the de-Sitter (dS) spacetime with the KR field and investigate the thermodynamic properties in the expanded phase space through introducing the interplay entropy between the black hole and cosmological horizons. Especially we analyze the effect of the Lorentz-violating parameter on the thermodynamic properties. Furthermore, the Lyapunov exponent and the shadow of these static and spherically symmetric black holes in this Lorentz-violating gravity theory are also investigated. These study will open a new perspective to probe the thermodynamics of black holes.

Shadow and weak gravitational lensing of RN-like BH in plasma

In this paper, we investigate weak gravitational lensing and shadow radius in the Kalb–Ramond (KR) gravity for an Reissner–Nordström-like (RN-like) black hole (BH). The examination is carried out in three distinct frameworks: uniform plasma, singular isothermal sphere(SIS), and non-singular isothermal sphere (NSIS). When a gravitating object is surrounded by plasma, the lensing angle is determined by the frequency of the electromagnetic wave, plasma dispersion, plasma inhomogeneity, and gravity. Even in uniform plasma, the gravitational photon deflection angle differs from that in a vacuum and depends on photon frequency due to the second effect. We consider both effects and calculate the lensing angle for a significantly non-uniform plasma in the existence of KR gravity. Utilizing observational data from the Event Horizon Telescope (EHT) project for Sgr A*, we have obtained that which range of RN-like black hole’s parameters Q and l correspond observations as well as when the Lorentz-violating parameter l rise, radius of black hole shadow decrease. To connect a relationship with observations data, we examine the magnification and positioning of images produced by lensing, as well as the weak deflection angle and magnification for sources located near various galaxies.

Entropy correction of Kerr–Newman-AdS black hole in Rastall gravity under Lorentz symmetry violation

The tunneling of scalar particles and fermions across the event horizon of KN-AdS black hole surrounded by perfect fluid in Rastall theory are investigated in the frame dragging coordinate systems by applying modified Klein–Gordon equation and modified Dirac equation under the influence of Lorentz symmetry violation in curved spacetime. The Hawking temperature and the heat capacity of the black hole are modified due to the influence of Lorentz symmetry violation. The Hawking temperature and the Bekenstein–Hawking entropy of the black hole beyond the semiclassical approximation are also derived by taking the effects of Planck constant [Formula: see text]. The modified Hawking temperature and entropy correction of the black hole are dependent on the Lorentz violation parameter [Formula: see text], the ether-like vectors [Formula: see text] and Planck constant [Formula: see text].

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a Schrödinger equation. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies

This study explores the impact of antisymmetric tensor effects on spherically symmetric black holes, investigating photon spheres, shadows, emission rate and quasinormal frequencies in relation to a parameter which triggers the Lorentz symmetry breaking. We examine these configurations without and with the presence of a cosmological constant. In the first scenario, the Lorentz violation parameter, denoted as λ, plays a pivotal role in reducing both the photon sphere and the shadow radius, while also leading to a damping effect on quasinormal frequencies. Conversely, in the second scenario, as the values of the cosmological constant (Λ) increase, we observe an expansion in the shadow radius. Also, we provide the constraints of the shadows based on the analysis observational data obtained from the Event Horizon Telescope (EHT) focusing on Sagittarius A* shadow images. Additionally, with the increasing Λ, the associated gravitational wave frequencies exhibit reduced damping modes.

Search for Lorentz violations through the sidereal effect at the NOνA experiment

Long-baseline neutrino oscillation experiments offer a unique laboratory to test the fundamental Lorentz symmetry, which is at the heart of both the standard model of particle and general relativity theory. The sidereal modulation in neutrino events will act as the smoking-gun experimental signature of Lorentz and CPT violation. In this study, we investigate the impact of the sidereal effect on standard neutrino oscillation measurements within the context of the NuMI Off-Axis νe Appearance Experiment (NOνA) experiment. Additionally, we assess the sensitivity of the NOνA experiment to detect Lorentz-violating interactions, taking into account the sidereal effect. Furthermore, we highlight the potential of the NOνA experiment to set new constraints on anisotropic Lorentz-violating parameters. Published by the American Physical Society 2024

Constraints on Lorentz violation parameter through electric dipole moments

The electric dipole moments of leptons (l-EDMs) could arise from the electrodynamics part of standard model extension (SME). In this work, we investigate the cross section of electron-positron collision in the Lorentz violation (LV) background via the l-EDMs. We find that the Lorentz violation parameter magnitudes constraint using LEP data to the level of |dLVe|<3.6×10-17\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|d^{e}_{LV}| < 3.6 \ imes 10^{-17} $$\\end{document}, |dLVμ|<9.5×10-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ |d^{\\mu }_{LV}|< 9.5 \ imes 10^{-10} $$\\end{document}, and |dLVτ|<1.5×10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ |d^{\ au }_{LV}|< 1.5 \ imes 10^{-6} $$\\end{document} for electron, muon, and tau, respectively. Moreover, we show the time-location dependence of muon-EDMs and tau-EDMs in the LV background. Therefore, upper bounds for combinations of LV parameters are obtained by current and future terrestrial experiments.

Gravitational traces of bumblebee gravity in metric–affine formalism

This work explores various manifestations of bumblebee gravity within the metric–affine formalism. We investigate the impact of the Lorentz violation parameter, denoted as X, on the modification of the Hawking temperature. Our calculations reveal that as X increases, the values of the Hawking temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the quasinormal modes, we employ the Wentzel–Kramers–Brillouin method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz–violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the quasinormal spectrum on time–dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time–domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of X correspond to larger shadow radii. Furthermore, we constrain the magnitude of the shadow radii using the EHT horizon–scale image of SgrA∗ . Finally, we calculate both the time delay and the deflection angle.

A new approach for limiting the Lorentz violation term (cμν) through analyzing e−e+ → μ−μ+ scattering in a strong magnetic field

The present study explores a novel approach to establish a new bound on the Lorentz violation parameter cμν in the muon sector. It is achieved by analyzing the scattering cross-section of electron-positron into muon-antimuon under the influence of a strong magnetic field while considering the anomalous magnetic moment. By the standard model extension, the detected discrepancy between the theoretical and experimental values of the anomalous magnetic moment can be attributed to Lorentz violation. New bounds on the Lorenz-violating coefficients cμν can be obtained by analyzing the theoretical scattering cross section's magnitude at a specific energy for both theoretical and experimental muon anomalous magnetic momentum values. The recently established bounds for the muon is around cTT+0.029cXX+0.07cYY+0.039cZZ<5.76×10−7.

On the Kalb–Ramond modified Lorentz violating hairy black holes and Thorne’s hoop conjecture

Recently, a class of static spherically symmetric power law corrected Lorentz violating (LV) Schwarzschild black holes in the Kalb–Ramond model have been derived and studied in the specific range of LV parameters (0<lambda le 2,Upsilon ge 0) that correspond to energy condition preserving (rho >0) source. On the other hand, there exist well known black holes that do not preserve the energy conditions. In this paper, we shall therefore relax energy conditions and numerically explore the horizon patterns of the enlarged class of LSMA black holes. Four generic types of LV corrected black holes emerge, which interestingly include the analogue of the braneworld black hole (rho <0) lending to Upsilon a new interpretation of “tidal charge” known as an imprint from the 5d bulk in the Randall–Sundrum scenario. We shall then show that Thorne’s hoop conjecture, mathcal {H} le 1, where mathcal {H} is the Hod function, consistently holds for three types and their generalizations. However, intriguingly, it turns out that, for the remaining type (viz., Schwarzschild–de Sitter and its generalizations), the hoop conjecture does not hold. It is also shown that braneworld tidal charge black holes increases the LV correction to planetary perihelion advance in contrast to the decrease due to ordinary black holes thereby providing a qualitative distinction between them.

Fermionic greybody factors and quasinormal modes of black holes in Kalb–Ramond gravity

In non-minimally coupled Kalb–Ramond (KR) fields, the vacuum expectation value (VEV) leads to spontaneous local Lorentz symmetry violation, resulting in static spherically symmetric solution. In this solution, fermionic greybody factors (GFs) and quasinormal modes (QNMs) are investigated. First, we study the wave dynamics of fermions using the Dirac and Rarita–Schwinger equations. We have derived the equations of effective potential for fermions with different spins. The fermionic GFs radiated by the black holes (BHs) are calculated using rigorous bounds as well as semi-analytic methods. The fermionic QNM of spin- 1/2 of the BHs in the KR gravity was analyzed using the sixth order WKB method. Furthermore, we discuss how Lorentz violating (LV) parameters impact GFs and QNMs. According to our results, the effective potential curve increases significantly when the LV parameter value γ is high. Thus, as the LV parameter γ increases, the bound of the GF and the QNM’s wave oscillation frequency will increase, while the decay rate will slow down.

A Lorentz-violating low-energy model for the bilayer graphene

In this work, we propose a model with Lorentz symmetry violation which describes the electronic low energy limit of the AA-bilayer graphene (BLG) system. The AA-type bilayer is known to preserve the linear dispersion relation of the graphene layer in the low energy limit. The theoretical model shows that in the BLG system, a time-like vector can be associated with the layer separation and contributes to the energy eigenstates. Based on these properties, we can describe in a $(2+1)$-dimensional space-time the fermionic quasi-particles that emerge in the low-energy limit with the introduction of a Lorentz-violating parameter, in analogy with the $(3 + 1)$-dimensional Standard Model Extension (SME). Moreover, we study the consequences of the coupling of these fermionic quasi-particles with the electromagnetic field, and we show via effective action that the low-energy photon acquires a massive spectrum. Finally, using the hydrodynamic approach in the collisionless limit, one finds that the LSV generates a new kind of anomalous thermal current to the vortexes of the system via coupling of the LSV vector.

Perturbative aspects of CPT -even Lorentz-violating scalar chromodynamics

In this work, we formulate the theory of Lorentz-violating scalar Quantum Chromodynamics with an arbitrary non-Abelian gauge group. This theory belongs to the class of models encompassed by the standard model extension framework. At the lowest order in the theory's Lorentz violation parameters, we calculate the divergent quantum corrections, including the renormalization group $\beta$-functions of the theory. The Lorentz-violating sector is shown to be scale invariant if there is a particular relation between the couplings.

Dark matter spike around Bumblebee black holes

The effects of dark matter spike in the vicinity of the supermassive black hole, located at the center of M87 (the Virgo A galaxy), are investigated within the framework of the so-called Bumblebee Gravity. Our primary aim is to determine whether the background of spontaneous Lorentz symmetry breaking has a significant effect on the horizon, ergo-region, and shadow of the Kerr Bumblebee black hole in the spike region.For this purpose, we first incorporate the dark matter distribution in a Lorentz-violating spherically symmetric space-time as a component of the energy-momentum tensors in the Einstein field equations. This leads to a space-time metric for a Schwarzschild Bumblebee black hole with a dark matter distribution in the spike region and beyond. Subsequently, this solution is generalized to a Kerr Bumblebee black hole through the use of the Newman-Janis-Azreg-Aïnou algorithm.Then, according to the available observational data for the dark matter spike density and radius, and the Schwarzschild radius of the supermassive black hole in Virgo A galaxy, we examine the shapes of shadow and demonstrate the influence of the spin parameter a, the Lorentz-violating parameter ℓ and the corresponding dark matter halo parameters ρ 0 and r 0 on the deformation and size of the shadow.

Probing Lorentz-violating electrodynamics with CMB polarization

We perform a comprehensive study of the signatures of Lorentz violation in electrodynamics on the Cosmic Microwave Background (CMB) anisotropies. In the framework of the minimal Standard Model Extension (SME), we consider effects generated by renormalizable operators, both CPT-odd and CPT-even. These operators are responsible for sourcing, respectively, cosmic birefringence and circular polarization. We propagate jointly the effects of all the relevant Lorentz-violating parameters to CMB observables and provide constraints with the most recent CMB datasets. We bound the CPT-even coefficient to kF,E+B < 2.31 × 10-31 at 95% CL. This improves previous CMB bounds by one order of magnitude. The limits we obtain on the CPT-odd coefficients, i.e. |k (3) (V)00| < 1.54 × 10-44 GeV and |kAF | < 0.74 × 10-44 GeV at 95% CL, are respectively one and two orders of magnitude stronger than previous CMB-based limits, superseding also bounds from non-CMB searches. This analysis provides the strongest constraints to date on CPT-violating coefficients in the minimal SME from CMB searches.

Three- and four-point functions in CPT -even Lorentz-violating scalar QED

The renormalization of quantum field theories usually assumes Lorentz and gauge symmetries, besides the general restrictions imposed by unitarity and causality. However, the set of renormalizable theories can be enlarged by relaxing some of these assumptions. In this work, we consider the particular case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this theory, we calculate the one-loop radiative corrections to the three- and four-point scalar-vector vertex functions, at the lowest order in the Lorentz violation parameters; and we explicitly verify that the resulting low-energy effective action is compatible with the usual gauge invariance requirements. With these results, we complete the one-loop renormalization of the model at the leading order in the Lorentz-violating parameters.

QNMs of slowly rotating Einstein–Bumblebee black hole

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 ell is similar to that of increasing the rotation parameter {tilde{a}}.

Analogy of the Lorentz-violating fermion-gravity and fermion photon couplings

By adopting a methodology proposed by R.J. Adler \etl, we study the interesting analogy between the fermion-gravity and the fermion-electromagnetic interactions in the presence of the minimal Lorentz-violating (LV) fermion coefficients. The one-fermion matrix elements of gravitational interaction (OMEGI) are obtained with a prescribed Lense-Thirring (LT) metric assuming test particle assumption. Quite distinct from the extensively studied linear gravitational potential, the LT metric is an essentially curved metric, and thus reveals the anomalous LV matter-gravity couplings as a manifestation of the so-called gravito-magnetic effects, which go beyond the conventional equivalence principle predictions. By collecting all the spin-dependent operators from the OMEGI with some reasonable assumptions, we get a LV non-relativistic Hamiltonian, from which we derive the anomalous spin precession and gravitational acceleration due to LV. Combined these results with certain spin gravity experiments, we get some rough bounds on several LV parameters, such as $|3\vec{\tilde{H}}-2\vec{b}|\leq1.46\times10^{-5}\mathrm{eV}$, with some ad hoc assumptions.