Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics
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Springer
Received: November 23, Revised: December 17, Accepted: December 17, Published: January 2,
2019 2019 2019 2020
M. Shokri IPM, School of Particles and Accelerators, P.O. Box 19395-5531, Tehran, Iran
E-mail: [email protected] Abstract: We present a generalization of the Bantilan-Ishi-Romatschke (BIR) solution of relativistic hydrodynamics to relativistic magnetohydrodynamics (RMHD). Using the symmetries of the boundary of the Kerr-AdS5 black hole, and certain simplifying assumptions we solve the equations of RMHD on this boundary for a highly conductive fluid. We then transform the resulting solution to the flat spacetime. Furthermore, we show that the force-free condition causes the magnetic field to become singular at particular points and propose a regularization process for removing the singularities. The regularization process reveals the importance of non-vanishing electrical current in RMHD. Keywords: Conformal and W Symmetry, Holography and quark-gluon plasmas, QuarkGluon Plasma, Space-Time Symmetries ArXiv ePrint: 1911.06196
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)011
JHEP01(2020)011
Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics
Contents 1 Introduction
1
2 BIR solution to hydrodynamics 2.1 Passing to flat spacetime 2.2 Milne coordinates
3 6 9 9 10 12 14
4 Passing to flat spacetime
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5 Regulaziation with sources
17
6 Numerical results
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7 Concluding remarks
25
A Choice of the hydro frame A.1 Landau frame A.2 Kovtun’s general frame
26 26 27
1
Introduction
It is expected that high energy collisions of heavy ions produce enormous electromagnetic fields, probably stronger than any other known electromagnetic fields in nature [1, 2]. Simulations suggest that the produced magnetic field is on order of 1018 −1020 Gauss and linearly proportional to the collision energy [3–6]. The estimated magnetic characteristic √ length [7], i.e. 1/ eB,1 at its peak is comparable to the typical length scale of strong interactions at low energies, namely 1/ΛQCD . This remark has led to dozens of studies on the probable effects of the magnetic field on the observables of the heavy-ion collisions [8– 12]. Most of the aforementioned works are based on the assumption of a static long-lasting magnetic field. This assumption, however, may not be realistic [13] and we can understand its unrealistic essence by a simple estimation. Consider eB being of the order of m2π 2 in the timescales that the QGP is formed. Such an assumption gives rise to an Alfven velocity [14] of the same order as the speed of sound. If that would be the case, the electromagnetic 1 2
Here B is the magnitude of the magnetic field and e is proton’s electric charge. mπ is Pion’s mass.
–1–
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3 Ideal MHD on the boundary 3.1 Force-free condition 3.2 Current-free solution 3.3 Gauge potential and magnetic helicity
–2–
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forces could compete with the pressure gradient in the determination of fluid kinematics. Since relativistic hydr
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