Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics

Abstract

In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz, which generalizes the well-known Hwa-Bjorken solution, we obtain a wide class of new exact, explicit and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects (i.e. the work done by the pressure and the modified change of the volume elements) into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, 1+1 dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we show that this general solution is stable for perturbations.

Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

“…After we have sent the first version of our manuscript to the journal the paper [10] was published 3 containing new interesting RHD solutions. Some of the solutions obtained in the present paper were independently found in [10] using different methods.…”

“…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 ).…”