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arXiv 1607.05935astro-ph.HE
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广义相对论中的强磁化旋转偶极子

Strongly magnetized rotating dipole in general relativity

J. Petri

摘要:

电磁波出现在物理学的许多领域。在一般情况下很难找到解决办法。本文在三维球极坐标系中数值积分了麦克斯韦方程组。简单的有限差分法将导致沿极轴的坐标奇异性。谱方法更适合处理与坐标系选择相关的人为奇异性。当辐射物体像恒星一样旋转时,麦克斯韦方程组的特殊类型的解值得研究,例如准静止状态。此外,在高能天体物理学中,特别是在旋转的中子星周围存在着强引力场和磁场。为了研究这类系统,我们设计了一种算法来求解球极坐标下的含时麦克斯韦方程组,包括广义相对论以及对首阶的量子电动力学修正。作为一个诊断,我们计算的自旋光度预期从这些恒星,并比较它的经典,即非相对论和非量子力学的结果。结果表明,即使磁场在$\numprint{4.4e9}$ ~ \si{\tesla}的临界值附近,量子电动力学也导致自旋下降光度的不相关变化.因此,制动指数保持接近于真空中的点偶极子的值,即$n=3$。同样的结论也适用于广义相对论量子电动力学修正的无力磁层。

英文摘要:

Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference methods would lead to a coordinate singularity along the polar axis. Spectral methods are better suited to deal with such artificial singularities related to the choice of a coordinate system. When the radiating object is rotating like for instance a star, special classes of solutions to Maxwell equations are worthwhile to study such as quasi-stationary regimes. Moreover, in high-energy astrophysics, strong gravitational and magnetic fields are present especially around rotating neutron stars. In order to study such systems, we designed an algorithm to solve the time-dependent Maxwell equations in spherical polar coordinates including general relativity as well as quantum electrodynamical corrections to leading order. As a diagnostic, we compute the spindown luminosity expected from these stars and compare it to the classical i.e. non relativistic and non quantum mechanical results. It is shown that quantum electrodynamics leads to an irrelevant change in the spindown luminosity even for magnetic field around the critical value of $\numprint{4.4e9}$~\si{\tesla}. Therefore the braking index remains close to its value for a point dipole in vacuum namely $n=3$. The same conclusion holds for a general-relativistic quantum electrodynamically corrected force-free magnetosphere.

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