arXiv 0808.22712008-08-16gr-qc

发电机等离子体实验室中的Kerr-Schild黎曼声学黑洞

Kerr-Schild Riemannian acoustic black holes in dynamo plasma laboratory

Garcia de Andrade

备注：: Departamento de fisica teorica-if-uerj-Brasil

摘要：

在等离子体物理中，Alfven、发电机和声波以及广义相对论性黑洞的存在已被证实，这为研究发电机流中类似爱因斯坦引力的声学黑洞有效度规的存在提供了足够的动力。从非线性发电机方程出发，得到非齐次波动方程，其中非齐次因子与压缩因子的时间演化成正比。在有限雷诺数的Navier-Stokes情形下，拉伸等离子体流上也存在声学黑洞。在静磁情况下，发电机是边际的。模拟模型通常应用于超流模拟时空，而不是这里使用的等离子体设置。本文给出了发电机方程的耦合非线性等离子体流解，其中标量有效方程的有效黑洞解产生了磁场增长的虚部。因此，尽管磁场增长率的实部为负或为零，但由于磁场中存在时间振荡，因此该解表示慢发电机。因此，声学黑洞被证明肯定有助于发电机行动的有效等离子体时空。我们认为，一个快速发电机有效时空也可能包含一个声学黑洞。在平面波的情况下，有效度规可以转换成Kerr-Schild时空形式。在这个度量和发电机波的增长中明确给出了Killing对称性。

英文摘要：

Since Alfven, dynamo and sound waves and the existence of general relativistic black holes are well stablished in plasma physics, this provides enough motivation to investigate the presence of acoustic black-hole effective metric of analogue Einstein's gravity in dynamo flows. From nonlinear dynamo equations, one obtains a non-homogeneous wave equation where it is shown that the non-homogeneous factor is proportional to time evolution of the compressibility factor. In the Navier-Stokes case for a finite Reynolds number the acoustic black-holes also exists on the stretching plasma flows. In the magnetostatic case the dynamo is marginal. Analog models are usually applied to a superfluid analog spacetime, instead of the plasma setting used here. A coupled nonlinear plasma flow solution is found for the dynamo equation where the effective black hole solution of the scalar effective equation yields an imaginary part of the growth of magnetic field. Therefore though the real part of the growth rate of the magnetic field is negative or null, since there is a temporal oscillation in magnetic field, the solution represents a slow dynamo. Thus acoustic black holes are shown to definitely contribute to dynamo action of the effective plasma spacetime. It is suggested that a fast dynamo effective spacetime may also contain an acoustic black hole. I the case of planar waves the effective metric can be cast in Kerr-Schild spacetime form. The Killing symmetries are explicitly given in this metric and the growth of dynamo waves.

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摘要：

英文摘要：

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