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.

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.

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.

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.

From Dirac’s Aether to the Dirac Equation

In 1951, Dirac proposed a formalism for a Lorentz invariant Aether with a vacuum state that contains all possible velocity states at each space-time point. Dirac showed no explicit path from the Aether towards the Quantum Mechanics. In this paper, we demonstrate that Dirac’s proposed Aether can be described by a lattice of possible events in space-time built in the local Lorentz frame. The idealised case of single velocity state leads to the famous Dirac equation for a plane wave state and is compatible with quantum statistics. On the lattice, possible space-time events are connected by the Dirac spinors which provide the probability of observing an event. The inertial mass of a particle is shown to be equivalent to the density of possible events on the lattice. Variation of the lattice density of events modifies the metric and provides a space-time curvature leading to the Hilbert action associated with general relativity. In classical limit, the perturbation in the density of possible events of the Aether is proportional to the Newtonian gravitational potential.

Local PoincaréSymmetry in Gauge Theory of Gravity

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.

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.