New family of simple solutions of relativistic perfect fluid hydrodynamics

Abstract

A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is foundmore than 50 years after the previous similar result, the Landau-Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, HwaBjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions.

Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

“…Some of the solutions obtained in the present paper were independently found in [10] using different methods. In particular, our solution (35) corresponds to equations (24), (25) of [10] that have been obtained as an extension of "accelerating" solutions of [9]. Also, our solution (10) in the case of the plane flow and extremely stiff EOS is the same as solution (114), (115) of [10].…”

“…This case can be easily extended to negative x and/or to negative t. For λ = 1 we obtain ε = 2A 2 (x 2 − t 2 ), v = −t/x. This is a kind of external scaling solutions discussed in the papers [9,10]. In order to obtain strict inequality (9) and regular solutions ∀ x, t, the above power-law choice for ψ and χ may be replaced, e.g., by χ (x) = ψ (−x) ∼ exp(γx n ), where γ = const ∈ R, n is a positive integer.…”

“…This motivated different authors to look for more simple solutions to be used in models of multiple pion production [5,6,7,8]; these solutions have extensions to the case of spherical and cylindric symmetry. Recent interest to such solutions is due to high energy heavy ion collisions (see, e.g., [9,10,11]). …”

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.…”

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

“…Here we shall present its nonextensive relativistic version from the point of view of high energy collision physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The characteristic feature of such a processes is the production of a large number of secondaries (multiplicities at present approach ∼ 10 3 ).…”