Elliptic Flow, Kasner Universe and Holographic Dual of RHIC Fireball

We consider a holographic dual of hydrodynamics of N = 4 SYM plasma that undergoes non-isotropic three-dimensional expansion relevant to RHIC fireball. Our model is a natural extension of the Bjorken’s one-dimensional expansion, and it describes an elliptic flow whose v2 and eccentricity are given in terms of anisotropy parameters. Holographic renormalization shows that absence of conformal anomaly in the SYM theory constrains our local rest frame to be a Kasner spacetime whose extreme limit reproduces the one used in the Bjorken’s theory. The conformal invariance also makes the hydrodynamic equations independent of the anisotropy parameters. We show that the dual geometry determines some of the hydrodynamic quantities in terms of the initial condition and the fundamental constants. ∗ E-mail: [email protected] † E-mail: [email protected] E-mail: [email protected]