Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics
- 26 Downloads
Motivated by the recently found realization of the 1 + 1 dimensional Bjorken flow in ideal and nonideal relativistic magnetohydrodynamics (MHD), we use appropriate symmetry arguments, and determine the evolution of magnetic fields arising from the 3 + 1 dimensional self-similar and Gubser flows in an infinitely conductive relativistic fluid (ideal MHD). In the case of the 3 + 1 dimensional self-similar flow, we arrive at a family of solutions, that are related through a differential equation arising from the corresponding Euler equation. To find the magnetic field evolution from the Gubser flow, we solve the MHD equations of a stationary fluid in a conformally flat dS3 × E1 spacetime. The results are then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the resulting magnetic field is shown to exhibit a transition between an early time 1/t decay to a 1/t3 decay at a late time. Here, t is the time coordinate. Transverse and longitudinal components of the magnetic fields arising from these flows are also found. The latter turns out to be sensitive to the transverse size of the fluid. In contrast to the result arising from the Gubser flow, the radial domain of validity of the magnetic field arising from the self-similar flow is highly restricted. A comparison of the results suggests that the (conformal) Gubser MHD may give a more appropriate qualitative picture of the magnetic field decay in the plasma of quarks and gluons created in heavy ion collisions.
KeywordsQuark-Gluon Plasma Conformal and W Symmetry Space-Time Symmetries
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- K. Yagi, T. Hatsuda and Y. Miake, Quark-gluon plasma: from big bang to little bang, Cambridge University Press, Cambridge U.K. (2005).Google Scholar
- J.D. Bjorken, Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region, Phys. Rev. D 27 (1983) 140 [INSPIRE].
- J.D. Bekenstein and E .Oron, New conservation laws in general-relativistic magnetohydrodynamics, Phys. Rev. D 18 (1978) 1809.Google Scholar
- L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics, Oxford University Press, Oxford U.K. (2013).Google Scholar
- L.D. Landau and E.M. Lifshitz, Fluid mechanics, second edition, Elsevier, Amsterdam Netherlands (1987).Google Scholar
- A. Zee, Einstein gravity in a nutshell, Princeton University Press, Princeton New Jersey U.S.A. (2013).Google Scholar
- S. Weinberg, Gravitation and cosmology: principles and applications of the general theory of relativity, John Wiley & Sons, Inc., New York U.S.A. (1972).Google Scholar
- C. Misner, K.S. Throne, J.A. Wheeler and D.I. Kaiser, Gravitation, W.H. Freeman and Co., San Fransisco U.S.A. (1973).Google Scholar
- M. Gedalin, Linear waves in relativistic anisotropic magnetohydrodynamics Phys. Rev. E 47 (1993)4354.Google Scholar
- G. Inghirami, L. Del Zanna, A. Beraudo, M. Haddadi Moghaddam, F. Becattini and M. Bleicher, Magneto-hydrodynamic simulations of Heavy Ion Collisions with ECHO-QGP, J. Phys. Conf. Ser. 1024 (2018) 012043 [INSPIRE].