Spontaneous Lorentz Symmetry Breaking Research Articles

Einstein–Bumblebee-dilaton black hole in Lifshitz spacetimes

We investigate the critical behavior of Lifshitz black holes in Einstein-dilaton gravity in the context of spontaneous Lorentz symmetry breaking. Considering the effects of both the Bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new asymptotically Lifshitz charged solutions in (3 + 1) dimensions. We consider the longitudinal massive mode of Lorentz violation (LV) as thermodynamic pressure, leading us to establish an P-V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P-V$$\\end{document} extended phase space. Within this framework, we derive the equation of state P(T, V), and subsequently identify the critical points, which manifest as discontinuities in the specific heat at constant pressure. Following this, we compute the Gibbs free energy, revealing a first-order phase transition within the model. Finally, we determine the critical exponents, demonstrating their equivalence to those observed in the Van der Waals system.

One-loop radiative corrections in bumblebee-Stueckelberg model

This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self-interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two-point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.

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.

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.

Investigating Lorentz Invariance Violation with the long baseline experiment P2O

One of the basic propositions of quantum field theory is Lorentz invariance. The spontaneous breaking of Lorentz symmetry at a high energy scale can be studied at low energy extensions like the Standard model in a model-independent way through effective field theory (EFT). The present and future Long-baseline neutrino experiments can give a scope to observe such a Planck-suppressed physics of Lorentz invariance violation (LIV). A proposed long baseline experiment, Protvino to ORCA (dubbed “P2O”) with a baseline of 2595 km, is expected to provide good sensitivities to unresolved issues, especially neutrino mass ordering. P2O can offer good statistics even with a moderate beam power and runtime, owing to the very large (~ 6 Mt) detector volume at KM3NeT/ ORCA. Here we discuss in detail, how the individual LIV parameters affect neutrino oscillations at P2O and DUNE baselines at the level of probability and derive analytical expressions to understand interesting degeneracies and other features. We estimate ∆χ2 sensitivities to the LIV parameters, analyzing their correlations among each other, and also with the standard oscillation parameters. We calculate these results for P2O alone and also carry out a combined analysis of P2O with DUNE. We point out crucial features in the sensitivity contours and explain them qualitatively with the help of the relevant probability expressions derived here. Finally we estimate constraints on the individual LIV parameters at 95% confidence level (C.L.) intervals stemming from the combined analysis of P2O and DUNE datasets, and highlight the improvement over the existing constraints. We also find out that the additional degeneracy induced by the LIV parameter aee around −22 × 10−23 GeV is lifted by the combined analysis at 95% C.L.

Exploring 2 + 2 answers to 3 + 1 questions

We explore potential uses of physics formulated in Kleinian (i.e. 2 + 2) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e. 3 + 1) signature. Much as Euclidean (i.e. 4 + 0) signature quantities can be used to formally construct the ground state wavefunction of a Lorentzian signature quantum field theory, a similar analytic continuation to Kleinian signature constructs a state of low particle flux in the direction of analytic continuation. There is also a natural supersymmetry algebra available in 2 + 2 signature, which serves to constrain the structure of correlation functions. Spontaneous breaking of Lorentz symmetry can produce various [Formula: see text] supersymmetry algebras that in 3 + 1 signature correspond to nonsupersymmetric systems. We speculate on the possible role of these structures in addressing the cosmological constant problem.

Testing the scalar sector of the standard-model extension with neutron gravity experiments

In the present study we analyse, within the scalar sector of the standard-model extension framework, the influence of a spontaneous Lorentz symmetry breaking on gravitational quantum states of ultracold neutrons. The model is framed according to the laboratory conditions of the recent high-sensitivity GRANIT and qBounce experiments. The high-precision data achieved in such experiments allow us to set bounds on the symmetry breaking parameters of the model. The effective Hamiltonian governing the neutron’s motion along the axis of free fall is derived explicitly. It describes a particle in a gravitational field with an effective gravitational constant controlled non-trivially by the Lorentz-violating parameters. In particular, using the exact wave functions and the energy spectrum, we evaluate both the heights associated with the quantum states and the transition frequencies between neighborhoring quantum states. By comparing our theoretical results with those reported in the GRANIT and the qBounce experiments, upper bounds on the Lorentz-violating parameters are determined. We also consider for the first time the gravity-induced interference pattern in a COW-type experiment to test Lorentz–invariance. In this case, an upper bound for the parameters is established as well.

Probing bumblebee gravity with black hole X-ray data

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 ell . We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter ell because of a very strong degeneracy between the estimates of ell and of the black hole spin parameter a_*. Such a degeneracy may be broken by combining other observations.

Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity

The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling ξ. The exact result for the fermionic determinant in the Einstein frame, including all orders in ξ, is also provided. We demonstrate that the axial contributions are at least of second order in the perturbative expansion of ξ. Furthermore, we compute the one-loop effective potential within the weak field approximation.

A prototypical nonlinear second-class system and its BFFT constraints Abelianization

We apply the Batalin–Fradkin–Fradkina–Tyutin formalism to a prototypical second-class system, aiming to convert its constraints from second class to first class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for feasible applications to field theory and mechanical models. The constraints can be arbitrarily nonlinear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As an explicit example, we discuss a spontaneous Lorentz symmetry breaking vectorial model, obtaining the full first-class Abelianized constraints in closed form and the corresponding involutive Hamiltonian.

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.

Spontaneous Lorentz Violation from Infrared Gravity

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.

Scalar Casimir effect for a conducting cylinder in a Lorentz-violating background

Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. The scalar field is modeled by a Lorentz-breaking extension of the theory for a real scalar quantum field in the bulk regions. The corresponding Green’s functions satisfying Dirichlet boundary conditions on the cylindrical shell are derived explicitly. We express the Casimir pressure (i.e. the vacuum expectation value of the normal–normal component of the stress–energy tensor) as a suitable second-order differential operator acting on the corresponding Green’s functions at coincident arguments. The divergences are regulated by making use of zeta function techniques, and our results are successfully compared with the Lorentz invariant case. Numerical calculations are carried out for the Casimir pressure as a function of the Lorentz-violating coefficient, and an approximate analytical expression for the force is presented as well. It turns out that the Casimir pressure strongly depends on the Lorentz-violating coefficient and it tends to diminish the force.

Black hole superradiance in the presence of Lorentz symmetry violation

In this paper we consider the massive scalar perturbation on the top of a small spinning-like black hole in context of Einstein-bumblebee modified gravity in order to probe the role of spontaneous Lorentz symmetry breaking on the superradiance scattering and corresponding instability. We show that at the low-frequency limit of the scalar wave the superradiance scattering will be enhanced with the Lorentz-violating parameter $\alpha<0$ and will be weakened with $\alpha>0$. Moreover, by addressing the black hole bomb issue, we extract an improved bound in the instability regime indicating that $\alpha<0$ increases the parameter space of the scalar field instability, while $\alpha>0$ decreases it.

Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry

We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebański, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.

Gödel-type universes in bumblebee gravity

The bumblebee field coupled with gravity is considered. This gravitational theory exhibits spontaneous breaking of Lorentz symmetry. The Gödel-type universe is introduced and then the causality and its violation are studied. Causal and noncausal Gödel-type solutions are obtained for different content of matter. In addition, when the coupling constant, which controls the interaction between the bumblebee field and the gravitational field, is zero the bumblebee potential may be associated with the value of the cosmological constant of the general relativity. Furthermore, the case with the nonzero coupling constant is also investigated.

Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking

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 r_c decreases with the Lorentz breaking constant ell >0, and increases with ell <0. These shifts are similar to those of Einstein-aether black hole. The effect of the LV parameter on the black hole shadow is that it accelerates the appearance of shadow distortion, and could be detected by the new generation of gravitational antennas.

Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking

Many current models which ``violate Lorentz symmetry'' do so via a vector or tensor field which takes on a vacuum expectation value, thereby spontaneously breaking the underlying Lorentz symmetry of the Lagrangian. One common way to construct such a model is to posit a smooth potential for this field; the natural low-energy solution of such a model would then be excepted to have the tensor field near the minimum of its potential. It is shown in this work that some such models, while appearing well posed at the level of the Lagrangian, have a Hamiltonian which is singular on the vacuum manifold and are therefore ill posed. I illustrate this pathology for an antisymmetric rank-2 tensor field and find sufficient conditions under which this pathology occurs for more general field theories.

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.