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 (DR) with the dimensionless parameter n = 2 and the "sign of LIV" {\eta}_+ = 1, to phenomenologically study the effect of quantum gravity in the 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 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.Comment: 18 pages, 7 figure

Some stability properties of T. Chan’s preconditioner

AbstractA matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we give some sufficient and necessary conditions for the stability of T. Chan’s preconditioner cU(An)

Nonlocal vibration of embedded double-layer graphene nanoribbons in in-phase and anti-phase modes

Graphene nanoribbons (GNRs), the finite-wide counterparts of crystalline graphene sheets, have been potential materials used in nano-devices because of their excellent electronic, thermal and mechanical properties. In this work, a theoretical analysis of nonlocal elasticity theory for the free vibrational characteristics of embedded double-layer GNRs (DLGNRs) is proposed based on continuum and Winkler spring models. We find two types of vibrational modes, in-phase mode (IPM) and anti-phase mode (APM). The results show that the vibrational properties of DLGNRs show different behaviors in IPM and APM. The natural frequencies of DLGNR embedded in an elastic matrix are significantly influenced by nonlocal effects, the aspect ratio of DLGNRs and the Winkler foundation modulus.ArticlePHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES. 44(7-8):1136-1141 (2012)journal articl