Lorentz Invariance Research Articles

Frequency- and polarization-dependent lensing of gravitational waves in strong gravitational fields

The propagation of gravitational waves can be described in terms of null geodesics by using the geometrical optics approximation. However, at large but finite frequencies the propagation is affected by the spin-orbit coupling corrections to geometrical optics, known as the gravitational spin Hall effect. Consequently, gravitational waves follow slightly different frequency- and polarization-dependent trajectories, leading to dispersive and birefringent phenomena. We study the potential for detecting the gravitational spin Hall effect in hierarchical triple black hole systems, consisting of an emitting binary orbiting a more massive body acting as a gravitational lens. We calculate the difference in time of arrival with respect to the geodesic propagation and find that it follows a simple power-law dependence on frequency with a fixed exponent. We calculate the gravitational spin Hall-corrected waveform and its mismatch with respect to the original waveform. The waveform carries a measurable imprint of the strong gravitational field if the source, lens, and observer are sufficiently aligned, or for generic observers if the source is close enough to the lens. We present constraints on dispersive time delays from GWTC-3, translated from limits on Lorentz invariance violation. Finally, we address the sensitivity of current and future ground detectors to dispersive lensing. Our results demonstrate that the gravitational spin Hall effect can be detected, providing a novel probe of general relativity and the environments of compact binary systems. Published by the American Physical Society 2024

Modification entropy of Kerr–Sen-like black hole in Lorentz-breaking bumblebee gravity

The Lorentz symmetry breaking theory not only affects the space–time background but also the dynamic behavior of bosons and fermions in curved space–time. Therefore, the Lorentz symmetry breaking theory will affect the quantum tunneling rate, Hawking temperature, black hole entropy, and other physical quantities of black holes. According to the modification of the space–time background and the modification of the particle dynamic equations, the quantum tunneling radiation of the Kerr–Sen-like black hole in bumblebee gravitational theory and its related contents are deeply studied. The research methods and a series of new results obtained in this paper are discussed. This makes the research methods and conclusions in this paper of more astrophysical significance and reference value.

Gravitational waves effects in a Lorentz–violating scenario

This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self–interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non–minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space–like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space–like component of the background field leads to a third–order time derivative of the quadrupole moment, and the bounds for the Lorentz–breaking coefficients are estimated as well.

Classical gravitational anomalies of Liouville theory

We show that for classical Liouville field theory, diffeomorphism invariance, Weyl invariance and locality cannot hold together. This is due to a genuine Virasoro center, present in the theory, that leads to an energy-momentum tensor with non-tensorial conformal transformations, in flat space, and with a non-vanishing trace, in curved space. Our focus is on a field-independent term, proportional to the square of the Weyl gauge field, WμWμ, that makes the action Weyl-invariant and was disregarded in previous investigations of Weyl and conformal symmetry. We show this term to be related to the classical center of the Virasoro algebra. The mechanism uncovered here is a classical version of the quantum anomalous phenomenon: the generalization to curved space only allows to keep one of the two symmetries enjoyed by the flat space theory, either Lorentz (diffeomorphism) or conformal invariance.

A basic examination of the gauged model of the Floreanini-Jackiw chiral boson within the framework of BRST symmetry

We consider the gauged model of Floreanini-Jackiw chiral boson which is generated from the chiral boson with parameter-free Faddeevian anomaly. This model does not have a manifestly Lorentz co-variant structure. However, it is exactly solvable and has a physical subspace that is precisely Lorentz invariant. The recommendation of Mitra and Rajaraman makes this model gauge invariant in the usual phasespace. Additionally, Wess-Zumino terms for this model are constructed to make it gauge-invariant which allows BRST embedding of the resulting gauge-invariant theory. Despite the strange structural appearance of the models when viewed in terms of Lorentz covariance BRST invariant reformulation has been found possible. Additionally, it has been observed that being supplemented with BRST symmetry, anti-BRST symmetry plays a crucial role in pinpointing the specific symmetric physical states.

Spinorial description for Lorentzian hs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{hs} $$\\end{document}-IKKT

We introduce a novel spinorial description for the higher-spin gauge theory induced by the IKKT matrix model on an FLRW spacetime with Lorentzian signature, called Lorentzian hs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{hs} $$\\end{document}-IKKT theory. The new description is based on Weyl spinors transforming under the space-like isometry subgroup SL(2, ℂ) of the structure group SO(2, 4) ≃ SU(2, 2). It allows us to exploit the full power of the spinor formalism in Lorentzian signature, in contrast to a previous formalism based on the compact subgroup SU(2)L × SU(2)R of SU(2, 2). Some cubic vertices of the Yang-Mills sector and the corresponding scattering amplitudes are computed. We observe that the n-point (for n ≥ 4) tree-level amplitudes are typically non-trivial on-shell, but exponentially suppressed in the late-time regime. While Lorentz invariance of the higher-spin amplitudes is not manifest, it is expected to be restored by higher-spin gauge invariance.

Effects on neutrino propagation in space-time foam of D-branes revisited

Neutrinos from the cosmos have proven to be ideal for probing the nature of space-time. Previous studies on high-energy events of IceCube suggested that some of these events might be gamma-ray burst neutrinos, with their speeds varying linearly with their energy, implying also the coexistence of subluminal and superluminal propagation. However, a recent reanalysis of the data, incorporating revised directional information, reveals stronger signals that neutrinos are actually being slowed down compared to previous suggestion of neutrino speed variation. Thus, it is worth discussing its implications for the brane/string inspired framework of space-time foam, which has been used to explain previous observations. We revisit effects on neutrino propagation from specific foam models within the framework, indicating that the implied violation of Lorentz invariance could necessarily cause the neutrino to decelerate. We therefore argue that this sort of model is in agreement with the updated phenomenological indication just mentioned. An extended analysis of the revised IceCube data will further test these observations and stringy quantum gravity.

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.

Functional Forms for Lorentz Invariant Velocities

Lorentz invariance lies at the very heart of Einstein’s special relativity, and both the energy formula and the relative velocity formula are well-known to be invariant under a Lorentz transformation. Here, we investigate the spatial and temporal dependence of the velocity field itself u(x,t) and we pose the problem of the determination of the functional form of those velocity fields u(x,t) which are automatically invariant under a Lorentz transformation. For a single spatial dimension, we determine a first-order partial differential equation for the velocity u(x,t), which appears to be unknown in the literature, and we investigate its main consequences, including demonstrating that it is entirely consistent with many of the familiar outcomes of special relativity and deriving two new partial differential relations connecting energy and momentum that are fully compatible with the Lorentz invariant energy–momentum relations.

Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition

We formulate a model for quantum gravity based on the local Lorentz symmetry and general-coordinate invariance. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain an inverse vierbein. Under this postulate, only the spinor becomes a dynamical field, and no gravitational background field is introduced in the tree-level action. In this paper, after explaining the transformation rules of the local Lorentz and general-coordinate transformations in detail, a tree-level action is defined. We show that fermionic fluctuations can induce a nonvanishing gravitational background field. Published by the American Physical Society 2024

New Constraint for Isotropic Lorentz Violation from LHC Data

New calculations for the kinematics of photon decay to fermions under an isotropic violation of Lorentz invariance (LV), parametrized by the standard-model extension, are presented in this Letter and used to interpret prompt photon production in LHC data. The measurement of inclusive prompt photon production at the LHC Run 2, with photons observed up to a transverse energy of 2.5 TeV, provides the lower bound κ˜tr>−1.06×10−13 on the isotropic coefficient κ˜tr at 95% confidence level. This result improves over the previous bound from hadron colliders by a factor of 55. The calculations for the kinematics of photon decay have further potential use to constrain LV coefficients from the appearance of fermion pairs. Published by the American Physical Society 2024

On the nonlinear electrodynamics in a Lorentz-breaking scenario

In this work, we study a model in nonlinear electrodynamics in the presence of a CPT-even term that violates Lorentz symmetry. The Lorentz-breaking vector, in addition to the usual background magnetic field, produces interesting effects in the dispersion relations. The consequences on the vacuum refractive index and the group velocity are studied. Vacuum birefringence is discussed in the case the nonlinear electrodynamics is a Euler–Heisenberg model.

Unraveling generalized parton distributions through Lorentz symmetry and partial DGLAP knowledge

Relying on the polynomiality property of generalized parton distributions, which roots on Lorentz covariance, we prove that it is enough to know them at vanishing and low skewness within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi region to obtain a unique extension to their entire support up to a D term. We put this idea in practice using two methods: reconstruction using artificial neural networks and finite-elements methods. We benchmark our results against standard models for generalized parton distributions. In agreement with the formal expectation, we obtain very a accurate reconstruction for a maximal value of the skewness as low as 20% of the longitudinal momentum fraction. This result might be relevant for reconstruction of generalized parton distribution from experimental and lattice QCD data, where computations are, for now, restricted in skewness. Published by the American Physical Society 2024

Simulating electromagnetic cascades with Lorentz invariance violation

Lorentz invariance violation (LIV) is a phenomenon featuring in various quantum gravity models whereby Lorentz symmetry is broken at high energies, potentially impacting the behaviour of particles and their interactions. Here we investigate the phenomenology of LIV within the context of gamma-ray–induced electromagnetic cascades. We conduct detailed numerical simulations to explore the expected manifestations of LIV on gamma-ray fluxes, taking into account relevant effects such as pair production and inverse Compton scattering. Additionally, we consider processes forbidden in the standard model, namely vacuum Cherenkov emission and photon decay. Our analysis reveals that these modifications result in distinct characteristics within the measured particle fluxes at Earth, which have the potential to be observed in high-energy gamma-ray observations.

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.

Neutrino Lorentz invariance violation from cosmic fields

From a cosmological perspective, scalar fields are well-motivated dark matter and dark energy candidates. Several possibilities of neutrino couplings with a time-varying cosmic field have been investigated in the literature. In this work, we present a framework in which violations of Lorentz invariance (LIV) and CPT symmetry in the neutrino sector could arise from an interaction among neutrinos with a time-varying scalar field. Furthermore, some cosmological and phenomenological aspects and constraints concerning this type of interaction are discussed. Potential violations of Lorentz and CPT symmetries at present and future neutrino oscillation experiments such as IceCube and KM3NeT can probe this scenario.

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

Probing the interference between non-linear, axionic and space-time-anisotropy effects in the QED vacuum

In this paper, we pursue the investigation of a generic non-linear extension of axionic electrodynamics in a Carroll-Field-Jackiw (CFJ) scenario that implements Lorentz-symmetry violation (LSV). The model we inspect consists of an arbitrary non-linear electrodynamic action coupled to the axion field in presence of an anisotropy four-vector that realizes the breaking of Lorentz symmetry under the particle point of view. For the sake of our considerations, the non-linear electromagnetic field is expanded around a constant and uniform magnetic background up to second order in the propagating photon field. The focus of our attention is the study of the material properties of the vacuum in the particular case of a space-like CFJ 4-vector. The dispersion relations associated to the plane wave solutions are explicitly worked out in two situations: the magnetic background perpendicular and parallel to the wave direction. We extend these results to consider the analysis of the birefringence phenomenon in presence of non-linearity, the axion and the LSV manifested through the spatial anisotropy. Three specific proposals of non-linear electrodynamics are contemplated: Euler-Heisenberg (EH), Born-Infeld (BI) and the Modified Maxwell electrodynamics (ModMax). Throughout the paper, we shall justify why we follow the unusual path of connecting, in a single Lagrangian density, three pieces of physics beyond the Standard Model, namely, non-linearity, axions and LSV. We anticipate that we shall not be claiming that the simultaneous introduction of these three topics beyond the Standard Model will bring new insights or clues for the efforts to detect axions or to constrain parameters associate to both non-linear electrodynamics and LSV physics. Our true goal is to actually inspect and describe how axionic, non-linear and LSV effects interfere with one another whenever physical entities like group velocity, refraction indices, birefringence and effective masses of physical excitations are computed in presence of an external constant and homogeneous magnetic field.

Unifying ordinary and null memory

Based on a recently proposed reinterpretation of gravitational wave memory that builds up on the definition of gravitational waves pioneered by Isaacson, we provide a unifying framework to derive both ordinary and null memory from a single well-defined equation at leading order in the asymptotic expansion. This allows us to formulate a memory equation that is valid for any unbound asymptotic energy-flux that preserves local Lorentz invariance. Using Horndeski gravity as a concrete example metric theory with an additional potentially massive scalar degree of freedom in the gravitational sector, the general memory formula is put into practice by presenting the first account of the memory correction sourced by the emission of massive field waves. Throughout the work, physical degrees of freedom are identified by constructing manifestly gauge invariant perturbation variables within an SVT decomposition on top of the asymptotic Minkowski background, which will in particular prove useful in future studies of gravitational wave memory within vector tensor theories.

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.