坡印廷矢量、超坡印廷矢量、电磁学和广义相对论中的主要观测者
Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity
摘要：
在电磁学中，由观测者测量的坡印廷矢量的概念是众所周知的。广义相对论中的一个数学类比是外尔张量的超坡印廷矢量。（超）坡印廷矢量为零的观测者称为主观测者。当在一个给定的点上，电磁场是非零的，或者引力场是Weyl-Petrov I型或D型的时候，瞬时通过该点的主观测者总是存在的。我们调查这样的观察员的特征，并研究他们的关系，任意观察员。在非零电磁场的情况下，已知给定任何观测者，存在一个主观测者，它相对于第一个观测者沿其坡印廷矢量的方向运动。用超坡印廷代替坡印廷得到一个可能的引力类比;我们证明，当彼得罗夫型为D时，这种类比确实对任何观测者成立，但当彼得罗夫型为I时，这种类比只对一维观测者成立。我们提供的算法，以获得主要的观察者直接从电场和磁场（在电磁的情况下）或电磁部分的Weyl张量（在引力的情况下）相对于一个任意的观察者。发现在Petrov型D双对准非零Einstein-Maxwell场（包含所有经典荷电黑洞解）中，坡印亭矢量和超坡印廷矢量在每一点和对每一观测者都是对准的，且主观测者重合.我们的结果说明在简单的例子。
英文摘要：
In electromagnetism, the concept of Poynting vector as measured by an observer is well known. A mathematical analogue in general relativity is the super-Poynting vector of the Weyl tensor. Observers for which the (super-)Poynting vector vanishes are called principal. When, at a given point, the electromagnetic field is non-null, or the gravitational field is of Weyl-Petrov type I or D, principal observers instantaneously passing through that point always exist. We survey characterizations of such observers and study their relation to arbitrary observers. In the non-null electromagnetic case it is known that, given any observer, there is a principal observer which moves relative to the first in the direction of his Poynting vector. Replacing Poynting by super-Poynting yields a possible gravitational analogue; we show that this analogy indeed holds for any observer when the Petrov type is D, but only for a one-dimensional variety of observers when the Petrov type is I. We provide algorithms to obtain the principal observers directly from the electric and magnetic fields (in the electromagnetic case) or electric and magnetic parts of the Weyl tensor (in the gravitational case) relative to an arbitrary observer. It is found that in Petrov type D doubly aligned non-null Einstein-Maxwell fields (which include all classical charged black hole solutions) the Poynting and super-Poynting vectors are aligned, at each point and for each observer, and the principal observers coincide. Our results are illustrated in simple examples.
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