如何在广义相对论中描述 Sweet-Parker 模型
How to describe the Sweet-Parker model in general relativity
AI总结：
本文探讨了广义相对论框架下 Sweet-Parker 磁重联模型的描述，通过对比狭义相对论计算提出时空曲率不改变模型性质，但不同静止参考系的观测会修正重联率与 Lundquist 数及外流速度与 Alfven 速度的关系。
摘要：
磁重联作为一种有效释放磁能的物理过程，在众多复杂的天体物理系统中发生，这是当今的热门话题。由于磁重联被认为频繁发生在产生强引力场的致密物体周围的吸积流中，它现在被视为从旋转黑洞提取能量的实用机制，这促使人们考虑如何以广义相对论方式描述磁重联过程。在这项工作中，我尝试探索广义相对论中对最著名的磁重联理论模型之一 Sweet-Parker 模型的描述。我首先回顾了狭义相对论中的 Sweet-Parker 模型，并将计算重新组织为七个步骤，讨论了它们的广义相对论形式。基于一般性讨论和具体例子的结果，我在本工作中提出，Sweet-Parker 模型中的任何性质都不会被时空曲率所改变，这与先前工作的结论相反。然而相反，在不同静止参考系中的观测可能会带来修正。如果磁重联不是发生在观察者的静止参考系中，观察者会发现探测到的重联率与 Lundquist 数之间的关系，或者外流速度与 Alfven 速度之间的关系，与磁重联恰好发生在观察者静止参考系中时探测到的关系不同。
英文摘要：
It is a hot topic nowadays that magnetic reconnection, as a physical process to release magnetic energy effectively, occurs in numerous complicated astrophysical systems. Since the magnetic reconnection is thought to occur frequently in the accretion flow around compact objects which induce strong gravitational field, it is now regarded to be a practical mechanism to extract energy from rotation black holes, which motivates people to consider how to describe the process of magnetic reconnection in a generally relativistic way. In this work, I try to explore the description of Sweet-Parker model, one of the most famous theoretical models of magnetic reconnection, in general relativity. I begin with revisiting the Sweet-Parker model in special relativity and reorganize the calculations in seven steps, whose generally relativistic forms are discussed. I propose in this work, from the general discussions and consequences of specific examples, that no property in Sweet-Parker model would be modified by spacetime curvature, which is opposite to the conclusions in previous work. However, on the contrary, observation in different rest frames may bring modifications. If the magnetic reconnection occurs not in the rest frame of observer, the observer would find out that the detected relation between the reconnection rate and Lundquist number or that between outflow speed and Alfven velocity are not the same as the detected relations if the magnetic reconnection occurs just in the rest frame of observer.
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