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arXiv 0810.2691gr-qc
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作为定常电真空时空源的旋转和反转相对论薄盘

Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

Gonzalo García-Reyes, Guillermo A. González

摘要:

本文详细研究了无径向应力的无限延伸的电真空静止轴对称相对论薄圆盘的反转模型(CRM),当圆盘的能量动量张量的本征值为实量时,不存在热流。我们发现了一个一般的约束反转的切向速度需要铸造的表面能-动量张量的磁盘作为两个反转带电尘埃流体的叠加。然后,我们表明,在某些情况下,这个约束可以得到满足,如果我们采取的两个反向旋转的切向速度相等和相反,或采取的两个反向旋转的流沿电动测地线循环。然而,我们表明,在一般情况下,它是不可能采取的两个反向旋转的流体沿电测地线循环,也不采取两个反向旋转的切向速度相等和相反。一个简单的家庭模型的基础上的Kerr-Newman解决方案的反向旋转带电磁盘被认为是我们得到一些磁盘与CRM表现良好。我们还表明,从克尔-纽曼解决方案构建的磁盘可以解释,为所有的参数值,作为一个物质分布与电流和纯方位角压力没有热流。该模型是使用著名的“位移,切割和反射”的方法扩展到真空爱因斯坦-麦克斯韦方程组的解决方案。我们得到,在所有的情况下,与所有的能量条件一致的反转Kerr-Newman磁盘。

英文摘要:

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.

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