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Energy confinement for a relativistic magnetic flux tube in the ergosphere of a Kerr black hole

机译:相对论磁通管的能量限制   Kerr黑洞的ergosphere

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摘要

In the MHD description of plasma phenomena the concept of magnetic fieldlines frozen into the plasma turns out to be very useful. We present here amethod of introducing Lagrangian coordinates into relativistic MHD equations ingeneral relativity, which enables a convenient mathematical formulation for thebehaviour of flux tubes. With the introduction of these Lagrangian, so--called``frozen--in'' coordinates, the relativistic MHD equations reduce to a set ofnonlinear 1D string equations, and the plasma may therefore be regarded as agas of nonlinear strings corresponding to flux tubes. Numerical simulationshows that if such a tube/string falls into a Kerr black hole, then the leadingportion loses angular momentum and energy as the string brakes, and tocompensate for this loss, momentum and energy is radiated to infinity toconserve energy and momentum for the tube. Inside the ergosphere the energy ofthe leading part turns out to be negative after some time, and the rest of thetube then gets energy from the hole. In our simulations most of the compensatedpositive energy is also localized inside the ergosphere because the inwardspeed of the plasma is approximately equal to the velocity of the MHD wavewhich transports energy outside. Therefore, an additional physical process hasto be included which can remove energy from the ergophere. Magneticreconnection seems fills this role releasing Maxwellian stresses and producinga relativistic jet.
机译:在对等离子现象的MHD描述中,冻结成等离子的磁力线的概念非常有用。我们在这里介绍一种将拉格朗日坐标引入相对论性MHD方程的广义相对论的方法,这可以为通量管的行为提供方便的数学公式。随着这些拉格朗日坐标(所谓的``冻结''坐标)的引入,相对论的MHD方程简化为一组非线性一维弦方程,因此等离子体可被视为对应于通量管的非线性弦的气体。数值模拟表明,如果这样的管/弦落入Kerr黑洞中,则在弦制动时前导部分会失去角动量和能量,并且为了补偿这种损失,动量和能量会辐射到无穷远以节省管的能量和动量。经过一段时间后,在人体工程圈内部,前导部分的能量变为负能量,然后其余的电子管从孔中获取能量。在我们的模拟中,大多数补偿的正能量也位于人体工圈内部,因为等离子体的内向速度大约等于将能量传输到外部的MHD波的速度。因此,必须包括额外的物理过程,该过程可以从遍历中移除能量。磁重联似乎扮演了释放麦克斯韦应力和产生相对论射流的角色。

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