Based on the generalized uncertainty principle with maximum momentum arid minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the probl...Based on the generalized uncertainty principle with maximum momentum arid minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited. Applying this equation of state to the Tolman-Oppenheimer Volkoff （TOV） equation, the quantum gravitational effects on the cores of compact stars are discussed. In the center of compact stars, we obtain the singularity-free solution of the metric component, gtt ～-（1 ＋ 0.2185×r^2）. By numerically solving the TOV equation, we find that quantum gravity plays an important role in the region r～10^4α0（△x）min. Current observed masses of neutron stars indicate that the dimensionless parameter α0 cannot exceed 10^19.展开更多
As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* ...As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No ZYGX2009X008
文摘Based on the generalized uncertainty principle with maximum momentum arid minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited. Applying this equation of state to the Tolman-Oppenheimer Volkoff （TOV） equation, the quantum gravitational effects on the cores of compact stars are discussed. In the center of compact stars, we obtain the singularity-free solution of the metric component, gtt ～-（1 ＋ 0.2185×r^2）. By numerically solving the TOV equation, we find that quantum gravity plays an important role in the region r～10^4α0（△x）min. Current observed masses of neutron stars indicate that the dimensionless parameter α0 cannot exceed 10^19.
文摘As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.
