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.
Highlights
Forces could compete with the pressure gradient in the determination of fluid kinematics
We present a generalization of the Bantilan-Ishi-Romatschke (BIR) solution of relativistic hydrodynamics to relativistic magnetohydrodynamics (RMHD)
The magnetic fields are assumed to be external in the sense that they need not satisfy the Maxwell equations, Recently a novel exact analytical solution to relativistic hydrodynamics is presented in [37] that breaks rotational and longitudinal boost symmetries that are assumed by Bjorken and Gubser flows
Summary
This solution is obtained from an assumed duality between a particular solution to Einstein equations in five-dimensional spacetime, namely the Kerr-AdS5 solution, with the solution to the equations of fluid mechanics on the four-dimensional boundary. As it is shown in [37], the line element of Kerr-AdS5 has the following leading behavior at r → ∞. The fluid energy-momentum tensor is given by [39]. The first vector in (2.9) dictates that the fluid is stationary and in equilibrium To satisfy this condition any source of dissipation must vanish.
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