Exact Relativistic Ideal Hydrodynamical Solutions in (1+3)D with Longitudinal and Transverse Flows

Abstract

A new method for solving relativistic ideal hydrodynamics in (1+3)D is developed. Longitudinal and transverse radial flows are explicitly embedded and the hydrodynamic equations are reduced to a single equation for the transverse velocity field only, which is much more tractable. As an application we use the method to find analytically all possible solutions with power dependence on proper time and transverse radius. Possible application to the Relativistic Heavy Ion Collisions and possible generalizations of the method are discussed.

9 pages

References in corpus (36)

• New Forms of QCD Matter Discovered at RHIC
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Flow at the SPS and RHIC as a Quark Gluon Plasma Signature
• What RHIC Experiments and Theory tell us about Properties of Quark-Gluon Plasma ?
• Anisotropic transverse flow and the quark-hadron phase transition
• Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze out
• Why does the Quark-Gluon Plasma at RHIC behave as a nearly ideal fluid ?
• Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics
• Simulating elliptic flow with viscous hydrodynamics
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Physics of Strongly coupled Quark-Gluon Plasma
• Perfect Fluidity of the Quark Gluon Plasma Core as Seen through its Dissipative Hadronic Corona
• Relativistic hydrodynamics for heavy-ion collisions
• Strongly coupled plasma with electric and magnetic charges
• Angular Dependence of Jet Quenching Indicates Its Strong Enhancement Near the QCD Phase Transition
• Magnetic Component of Quark-Gluon Plasma is also a Liquid!
• Magnetic component of Yang-Mills plasma
• Landau Hydrodynamics Reexamined
• What do lattice baryonic susceptibilities tell us about quarks, diquarks and baryons at $T>Tc$?
• An introduction to relativistic hydrodynamics
• Unified description of Bjorken and Landau 1+1 hydrodynamics
• Magnetic monopoles in the high temperature phase of Yang-Mills theories
• Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics
• Electric Flux Tube in Magnetic Plasma
• Polymer Chains and Baryons in a Strongly Coupled Quark-Gluon Plasma
• Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics
• Microscopic formula for transport coefficients of causal hydrodynamics
• A Co-moving Coordinate System for Relativistic Hydrodynamics
• Generating new solutions for relativistic transverse flow at the softest point
• Analytic solution for relativistic transverse flow at the softest point
• Exposing the Noncollectivity in Elliptic Flow
• Hot and dense matter: from RHIC to LHC: Theoretical overview
• Ellipsoidal flows in relativistic hydrodynamics of finite systems
• Expansion rates at RHIC
• Similar final states from different initial states using new exact solutions of relativistic hydrodynamics
• Hydrodynamical activity in thin accretion disks

Cited by in corpus (9)

• Holographic Heavy-Ion Collisions: Analytic Solutions with Longitudinal Flow, Elliptic Flow and Vorticity
• Exact analytical solutions of second-order conformal hydrodynamics
• A systematic study of exact solutions in second-order conformal hydrodynamics
• Multipole solution of hydrodynamics and higher order harmonics
• A new family of exact and rotating solutions of fireball hydrodynamics
• New simple explicit solutions of perfect fluid hydrodynamics and phase-space evolution
• The "ripples" on relativistically expanding fluid
• Viscous effects on the dynamical evolution of QCD matter during the first-order confinement phase transition in heavy-ion collisions
• On Analytic Solutions of (1+3)D Relativistic Ideal Hydrodynamic Equations