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)

Radial breathing vibration of double-walled carbon nanotubes subjected to pressure

A theoretical vibrational analysis of the radial breathing mode (RBM) of double-walled carbon nanotubes (DWCNTs) subjected to pressure is presented based on an elastic continuum model. The results agree with reported experimental results obtained under different conditions. Frequencies of the RBM in DWCNTs subjected to increasing pressure depend strongly on circumferential wave numbers, but weakly on the aspect ratio and axial half-wave numbers. For the inner and outer tubes of DWCNTs, the frequency of the RBM increases obviously as the pressure increases under different conditions. The range of variation is smaller for the inner tube than the outer tube.ArticlePHYSICS LETTERS A. 375(24):2416-2421 (2011)journal articl