Researches On Critical Properties Of Black-hole Thermodynamics And Holographic Hydrodynamics Transport Coefcients

We studied the critical properties of black hole thermodynamics in Reissner-Nordstrom Anti-de Sitter background, and also discussed the simple operation on howto calculate the transport coefcients for the dual fluid which lived on cutof surface indiferent gravity systems. By comparing to the gas-liquid van der Waals systems, and byintroducing two functions T (n,k) and F(n,k), we analyzed the efects of cosmologicalconstant when adding it on the first law of black hole thermodynamics, and obtainedthe relation between critical coefcient and dimension, the function T (n, k) is a smal-l quantity and it can be thought of as the fluctuation which dependent on dimensions,the function F(n,k) can be regarded as the critical coefcients. On basis of black holethermodynamics, we studied on how to calculate the transport coefcients for dual flu-id which lived on cutof surface in the five-dimensional charge dilatonic black hole andsingle R-Charged black hole. By using the results from membrane paradigm and the ther-modynamic quantity from Brown-York tensor, we verified and obtained the formulae fortransport coefcients, these expression show that: once the metric gave in context, wecan directly obtain the result of transport coefcients with not to calculate the intermedi-ate variables. The formulae for retarded Green functions were also given in appendix Bin the last of paper.