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Summary
New results are shown in this paper on the pseudorapidity distributions and initial energy density estimate from the previous known exact solutions of accelerating hydrodynamic and Buda-Lund hydrodynamic model. We have extracted a series of acceleration parameter $\lambda$ for different systems at RHIC and LHC energies. Taking the acceleration effect into account and refining the typical Bjorken model, we got a general class of initial energy density $\varepsilon_{corr}$ for central collisions, which was found significantly lager based on the latest PHENIX and LHC transverse energy spectra.
An improved estimate for initial energy density is also discussed for the semi-central collisions. For peripheral collisions the estimate for the initial energy density is difficult based on the Bjorken model. Here we are able to find the approximation based on the MC-Glauber model and the initial accelerating time period. For the peripheral case there exist various qualitative and quantitative analyses, and the thermalization time, freeze-out time, transverse overlap, and volume expansion deserve more attention discussing the QGP medium initial energy density. The more detailed testing of QGP medium numerical solutions of peripheral collision will be done in the future.
It should be emphasized that in this paper our purpose is to discuss inhomogeneous flow from exact solution of relativistic hydrodynamics, and that the relativistic hydrodynamic Buda-Lund model can describe the experimental data stable and causally. Either analytically or numerically, the accelerating hydrodynamical description makes a difference on both the rapidity distribution and the energy density estimation.
