Comoving coordinate system for relativistic hydrodynamics

Abstract

The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving observers. Aside from the time step varying as a function of the location on the mesh, the local velocity gradient and the local density then evolve according to non-relativistic equations of motion. Analytic solutions are found for two onedimensional cases with constant speed of sound. One solution has a Gaussian density profile when mapped into the new coordinates. That solution is analyzed for the effects of longitudinal acceleration in relativistic heavy ion collisions at RHIC, especially in regards to two-particle correlation measurements of the longitudinal size.

Landau hydrodynamics reexamined

“…Landau hydrodynamics provides a plausible description for the evolution of the dense hot matter produced in high-energy heavy-ion collisions. Its dynamics during the first stage of the one-dimensional longitudinal expansion can be solved exactly and the one-dimensional longitudinal expansion problem admits simple approximate solutions [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The subsequent three-dimensional motion can be solved approximately to give rise to predictions that come close to experimental data [1,2,3,6,7].…”

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

“…The integral in Eq. (22) can be evaluated numerically as the limits of the integration and the integrands are known functions of ζ and y.…”

Perturbative Accelerating Solutions of Relativistic Hydrodynamics

“…Refs. [12][13][14] for recent examples), multiple advanced analytic solutions were found in the last decade [7,[15][16][17][18][19][20][21]. One important example is the simple, ellipsoidal Hubble-flow described in Ref.…”