How Kieffer Density Matrix Formalism Aids Different Initial Time Steps, Leading to Lorentz Violations, and Breakup of Primordial Black Holes for GW Generation

A result from Kieffer, as outlined at the beginning of the article identifies two different candidates for initial time steps, delta t. We assert that this difference in time steps may be related to a specific early universe Lorentz Violation. The author asserts that the existence of early universe Lorentz violation in turn is assisting in a breakup of primordial black holes. And that also has a tie into Kieffer different time steps as outlined. And the wrap up is given in the final part of this document.

Constraining Lorentz Invariance Violation Using Short Gamma-Ray Bursts

Lorentz Invariance is a foundational principle in modern physics, but some recent quantum gravity theories have hinted that it may be violated at extremely high energies. Gamma-ray bursts (GRBs) provide a promising tool for checking and constraining any deviations from Lorentz Invariance due to their huge energies and cosmological distances. Gamma-ray bursts, which are the most intense and powerful explosions in the universe, are traditionally divided into long bursts whose observed duration exceeds 2 s, and short bursts whose observed duration is less than 2 s. In this study, we employ a recent sample of 46 short GRBs to check for any deviation from Lorentz Invariance. We analyze the spectral lag of the bursts in our data sample and check for any redshift dependence in the GRB rest frame, which would indicate a violation of Lorentz Invariance. Our results are consistent, to within 1σ, with no deviation from Lorentz Invariance.

Uplifting of AdS type to quintessence-like potential induced by frozen large-scale Lorentz violation

The quintessence-like potential of vacuum energy can meet the requirements from both quantum gravity and the accelerating expansion of the universe.The anti-de Sitter(AdS)vacuum in string theory must be lifted to the meta-stable dS vacuum with a positive vacuum energy density to explain the accelerating expansion of the universe.Based on possible large-scale Lorentz violation,we define an effective cosmological constant that depends not only on the bare cosmological constant but also on the Lorentz violation effect.We find that the evolution of the effective cosmological constant exhibits the behavior of the quintessence potential when the bare cosmological constant originates from the string landscape,in contrast to the existence of a local minimum during evolution when the bare cosmological constant is supplied by the swampland.The critical value of the bare cosmological constant is approximately zero for the behavior transition.The frozen large-scale Lorentz violation can uplift the AdS vacua to an effective quintessence-like one in this sense.

Spatial curvature and large scale Lorentz violation

The tension between the Hubble constant values obtained from local measurements and cosmic microwave background(CMB)measurements has motivated us to consider the cosmological model beyondΛCDM.We investigate the cosmology in the large scale Lorentz violation model with a non-vanishing spatial curvature.The degeneracy among spatial curvature,cosmological constant,and cosmological contortion distribution makes the model viable in describing the known observational data.We obtain some constraints on the spatial curvature by comparing the relationship between measured distance modulus and red-shift with the predicted one,the evolution of matter density over time,and the evolution of effective cosmological constant.The implications of the large scale Lorentz violation model with the non-vanishing spatial curvature under these constrains are discussed.

Slowly rotating Einstein-bumblebee black hole solution and its greybody factor in a Lorentz violation model

We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding rr and tθ components of the gravitational field equations for both cases:A)b u=(0,b(r),0,0) and B) bu=(0,b(r),b(θ),0) .Then,we check the other gravitational field equations and the bumblebee field motion equations using this solution.We find that for case A,there indeed exists a slowly rotating black hole solution for an arbitrary LV(Lorentz violation)coupling constant l;however,for case B,this slowly rotating solution exists if and only if coupling constant l is as small as or smaller than angular momentum a.Thus far,no full rotating black hole solution has been published;hence,the Newman-Janis algorithm cannot be used to generate a rotating solution in the Einstein-bumblebee theory.This is similar to the Einstein-aether theory,wherein only some slowly rotating black hole solutions exist.To study the effects of this broken Lorentz symmetry,we consider the black hole greybody factor and find that,for angular index l=0 ,LV constant l decreases the effective potential and enhances the absorption probability,which is similar to the results for the non-minimal derivative coupling theory.

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL（2, C） and the Lorentz group via the Pauli grading （the elements of SL（2, C） expressed by direct sum of unit matrix and generators of SU（2） group）, we grade the SL（3,C） group with the generators of SU（3）, i. e. the Gell-Mann matrices, then express the SU（3） group in terms of three SU（2） subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL（2,C）. If the mapping from group SL（3,C） to the Lorentz group is constructed by choosing one SU（2） subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex -γμθ^μ is extended to encompass γ5γμθ^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.

Strong constraints on Lorentz violation using new γ-ray observations around PeV

The tiny modification of dispersion relation induced by Lorentz violation(LV)is an essential topic in quantum gravity(QG)theories,which can be magnified into significant effects when dealing with astrophysical observations at high energies and long propagation distances.LV would lead to photon decay at high energies;therefore,observations of high-energy photons could constrain LV or even QG theories.The Large High Altitude Air Shower Observatory(LHAASO)is the most sensitive gamma-array instrument currently operating above 100 TeV.Recently,LHAASO reported the detection of 12 sources above 100 TeV with maximum photon energy exceeding 1 PeV.According to these observations,the most stringent restriction is achieved in this study,i.e.,limiting the LV energy scale to 1.7×10^(33) eV,which is over 139,000 times that of the Planck energy,and achieving an improvement of approximately 1.9 orders of magnitude over previous limits.

Lorentz violation, quantum tunneling, and information conservation

In this paper, by introducing the Lorentz-invariance-violation(LIV) class of dispersion relations(DR)suppressed by the second power(E/EQG)2, we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordstrom(RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle. However, at the same energy level, it was insensitive to changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation.We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.

New theory of Lorentz violation from a general principle

We report that a general principle of physical independence of mathematical background manifolds brings a replacement of common derivative operators by co-derivative ones. Then we obtain a new Lagrangian for the ordinary minimal standard model with supplementary terms containing the Lorentz invariance violation information measured by a new matrix, denoted as the Lorentz invariance violation matrix. We thus provide a new fundamental theory to study Lorentz invariance violation effects consistently and systematically.

Electrodynamics with violations of Lorentz and U(1)gauge symmetries and their Hamiltonian structures

This study aims to investigate Lorentz/U(1)gauge symmetry-breaking electrodynamics in the framework of the standard-model extension and analyze the Hamiltonian structure for the theory with a specific dimension of Lorentz breaking operators.For this purpose,we consider a general quadratic action of the modified electrodynamics with Lorentz/gauge-breaking operators and calculate the number of independent components of the operators at different dimensions in gauge invariance and breaking.With this general action,we then analyze how Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension as examples.We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the theory constrains and the number of physical degrees of freedom of the standard Maxwell electrodynamics.When U(1)gauge symmetry-breaking operators are present,the theories generally lack a first-class constraint and have one additional physical degree of freedom compared to the standard Maxwell electrodynamics.

Maxwell's equal area law for Vaidya-Bonner-de Sitter black hole under Lorentz invariance violation

In this study,we investigate the tunneling of fermions with arbitrary spin near the event horizon of a nonstationary Vaidya-Bonner-de Sitter(VBdS)black hole under Lorentz invariance violation(LIV).The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation,Feynman prescription,and Wentzel-Kramers-Brillouin approximation.By considering the cosmological constant as a thermodynamic pressure in the extended phase space,we construct a Maxwell's equal area law under LIV and study the phase transitions of VBdS black hole in P-v,P-V,and T-S planes.The LIV increases the length of the liquid-gas coexistence region.The thermodynamic quantities such as the entropy,heat capacity,Helmholtz free energy,internal energy,enthalpy,and Gibbs free energy of the VBdS black hole are discussed.These quantities tend to increase under LIV.The stability of the black hole is also discussed in the presence of LIV.

Nonrelativistic quantum effects of the Lorentz symmetry violation on the Morse potential

We search for Lorentz symmetry violation effects at low-energy regime by exploring the Dirac equation in(1+1)-dimensions and the possibility of dealing with quantum systems with spherical symmetry.We bring a discussion about the influence of the Lorentz symmetry violation effects on the spectrum of molecular vibrations caused by the coupling between a fixed vector field and the derivative of the fermionic field.Further,we discuss the influence of this Lorentz symmetry violation background on the revival time.

Fermions dynamic equation with Lorentz invariance violation and the corrected Hawking temperature in arbitrarily accelerating black hole

Containing Lorentz invariance violation(LIV),a new form of the fermions dynamic equation under the background of the curved space-time of the arbitrarily accelerating black hole,is studied.Firstly,we consider the new form of the fermions dynamic equation with arbitrary spin containing LIV in curved space-time,and research the fermions dynamic equation with spin-1/2containing LIV.On this basis,according to the semi-classical theory and black hole quantum tunneling radiation theory,the quantum tunneling radiation of the arbitrarily accelerating Kinnersly black hole is modified correctly,and the corrected physical quantities such as black hole temperature and quantum tunneling rate are deeply discussed.The fermions dynamic equation with arbitrary spin in the arbitrarily accelerating black hole space-time and its solution are explained in detail.In order to further obtain the correction effect of the Planck scale,this article considers beyond the semi-classical theory and further obtains new expressions of the black hole temperature and tunneling radiation rate.

Long Range, Long Lived and Gauge Invariant Massive Photons via Stückelberg Scalar Coupling

It is largely believed (or strongly assumed) that photons are massless particles and the most compelling evidence there—it is said—is found in the manifestations of photons being long ranged and long lived particles. As we have done before, albeit, with a much better and clear insight in the present than before;we argue herein that massive photons can still enjoy the special and rare privilege of travelling at the speed of light c while being long ranged, long lived and most of all, obeying the much desired gauge symmetry. This we achieve by breaking the traditional Lorenz gauge and in its place, we introduce a new Special Gauge Condition (SGC) that does the work of assuring the photon its longevity, long range-ness and that it [photon] propagates at the speed c. However, the most melancholic outcome of our investigation is that if the present scheme is what subtle Nature has chosen to endow the photon a non-zero mass so that it [photon] still obeys gauge invariance, is long ranged, long lived and travels at the sacred speed c;then, this non-zero photon mass may be very difficult, if not impossible to measure. We use the equations developed to investigate Lorentz violation in ?-ray bursts.

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation（LIV）. As the most energetic explosions in the Universe, gamma-ray bursts（GRBs） provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB,we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M_（QG） 〉 5.05 × 10^（14） GeV in the linearly corrected case, is from GRB 140622 A. Our constraint on MQG,although not as tight as previous results, is the safest and most reliable so far.

Aharonov–Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field.This neutral particle is also under the influence of a background that breaks the Lorentz symmetry.We focus on the Lorentz symmetry violation background determined by a space-like vector field.Then,we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential.Furthermore,we obtain the bound state solutions to the SchrÖdinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase.Finally,we discuss the arising of persistent spin currents.

The effective potential originating from swampland and the non-trivial Brans-Dicke coupling

The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuumenergy density can be viewed as the energy density of the auxiliary quintessence field potential.We find thatthe negative bare vacuum energy density from string landscape leads to a monotonically decreasing quintessence potentialwhile the positive one from swampland leads to the metastable or stable de Sitter-like potential.Moreover,thenon-trivial Brans-Dicke like coupling between the quintessence field and gravitation field is necessary in the lattercase.

Note on a new fundamental length scale l instead of the Newtonian constant G

The newly proposed entropic gravity suggests gravity as an emergent force rather than a fundamental one. In this approach,the Newtonian constant G does not play a fundamental role any more, and a new fundamental constant is required to replace itsposition. This request also arises from some philosophical considerations to contemplate the physical foundations for the unificationof theories. We here consider the suggestion to derive G from more fundamental quantities in the presence of a new fundamentallength scale l, which is suspected to originate from the structure of quantum space-time, and can be measured directly from Lorentz-violating observations. Our results are relevant to the fundamental understanding of physics, and more practically, of natural units,as well as explanations of experimental constraints in searching for Lorentz violation.

Symmetries in a very special relativity and isometric group of Finsler space

We present an explicit connection between the symmetries in a Very Special Relativity （VSR） and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.