Note on Thermodynamics Method of Black Hole/CFT Correspondence

In the paper we further refine the thermodynamics method of black hole/CFT correspondence. We show that one can derive the central charges of different holographic pictures directly from the entropy product $S_+S_-$ if it is mass-independent, for a black hole in the Einstein gravity or the gravity without diffeomorphism anomaly. For a general black hole in the Einstein gravity that admits holographic descriptions, we show that the thermodynamics method and asymptotic symmetry group (ASG) analysis can always give consistent results in the extreme limit. Furthermore, we discuss the relation between black hole thermodynamics and the hidden conformal symmetry. We show that the condition $T_+A_+=T_-A_-$, with $A_\pm$ being the outer and inner horizon areas, is the necessary, but not sufficient, condition for a black hole to have the hidden conformal symmetry. In particular, for the Einstein(-Maxwell) gravity $T_+A_+=T_-A_-$ is just the condition $T_+S_+=T_-S_-$, with $S_\pm$ being the outer and inner horizon entropies, which is the condition for the entropy product $S_+S_-$ being mass-dependent. When there exists the hidden conformal symmetry in the low-frequency scattering off the generic non-extremal black hole, it always leads to the same temperatures of dual CFT as the ones got from the thermodynamics method.Comment: 31 pages, references added, published versio

The Regional Variation of Ontario Works: From the Perspective of Provincial-Municipal Relationship

This paper examines the regional variations of Ontario Works in the province using empirical studies of 12 municipalities: Durham, Halton, Hamilton, London, Muskoka, Niagara, Ottawa, Sudbury, Toronto, Waterloo, Windsor, and York. The findings reveal that the variation of Ontario Works in different municipalities is limited and the services provided to clients are similar across the entire province. Furthermore, in understanding why the provincial government still requires the involvement of municipalities in the program, despite it being consistent across Ontario, it concludes that the introduction of Ontario Works was accompanied by the province’s decentralization process and the fiscal retrenchment of provincial government in Ontario Works requires municipalities to have some autonomy

Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension

In the present paper, we investigate the dynamics of a Bose-Einstein condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both analytically and numerically. We focus on the self-trapping state and the effect of the system dimension. Under the tight-binding approximation we obtain an analytical criterion for the self-trapping state of BEC using time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of the BEC cloud is obtained accordingly and verified by directly solving the discrete Gross-Pitaevskii equation (GPE) numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the lattices.Comment: 8pages, 9 figure

The vertical composition of neutrino-dominated accretion disks in gamma-ray bursts

We investigate the vertical structure and elements distribution of neutrino-dominated accretion flows around black holes in spherical coordinates with the reasonable nuclear statistical equilibrium. According our calculations, heavy nuclei tend to be produced in a thin region near the disk surface, whose mass fractions are primarily determined by the accretion rate and the vertical distribution of temperature and density. In this thin region, we find that $^{56}\rm Ni$ is dominant for the flow with low accretion rate (e.g., $0.05$$M_{\odot}$ $\rm s^{-1}$) but $^{56}\rm Fe$ is dominant for the high counterpart (e.g., $1 M_{\odot}$ $\rm s^{-1}$). The dominant $^{56}\rm Ni$ in the special region may provide a clue to understand the bumps in the optical light curve of core-collapse supernovae.Comment: 15 pages, 2 figures, accepted for publication in Ap

6-Bromo­pyridine-2-carboxamide

In the the title compound, C6H5BrN2O, an intra­molecular N—H⋯N hydrogen bond generates an S(5) ring. In the crystal structure, inter­molecular bifurcated N—H⋯(O,O) hydrogen bonds link the mol­ecules, leading to sheets propagating in (100)