Class Of Dispersion Relations Research Articles

Lorentz violation, quantum tunneling, and information conservation * *Supported by the National Natural Science Foundation of China (11903025), and by the starting fund of China West Normal University (18Q062), and by the Natural Science Foundation of Sichuan Education Department (17ZA0294), and by the Research Project of Si Chuan MinZu College (XYZB18003ZA)

In this paper, by introducing the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power , we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordström (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.

An application of Lorentz-invariance violation in black hole thermodynamics

In this paper, we have applied the Lorentz-invariance violation (LIV) class of dispersion relations (DRs) with the dimensionless parameter textit{n}=2 and the “sign of LIV” eta _+ = 1, to a phenomenological study of the effect of quantum gravity in a strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the “reduced Bekenstein–Hawking entropy”, and the ill-defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared results with the earlier findings by another quantum-gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the inert remnants at the final stage of the black hole evaporation that, the GUP as a candidate for describing quantum gravity can always do as well as the LIV-DR by adjusting the model-dependent parameters, but in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.

A study of the dispersion relations for forward K ±p scattering

Forward dispersion relations, indexed by continuous parameters β and ω o, are written for the clasd of functions B ±( ω) = F ±( ω)/( ω ± m K) β ( ω ± ω o) 1− β , 0 ⩽ β ⩽ 1, 0 ⩽ ω o ⩽ m K, defined in terms of the K±p forward scattering amplitudes F± in the laboratory systerm. The value of the integral involving F _ over the unphysical region of energies below the K -p threshold is sensitively controlled by β and ω o, so that this class of dispersion relations ought to provide a good test of the extrapolation of a model amplitude into the unphysical region. We have used this method to test three models - a modifed constant scattering length analysis, a zero-range K-matrix analysis and an effective-range K-matrix analysis - but the usefulness of the test is found to be limited by the very poor D _ data currently available. Some comments are made about the estimation of the strange particle coupling constants appearing in the dispersion relations.