论文标题
凯尔时空的身体动机
Physically motivated ansatz for the Kerr spacetime
论文作者
论文摘要
尽管在Kerr旋转黑洞的主题上进行了60年的工作，但目前尚无广泛接受的基于物理的和教学上可行的ANSATZ，适合在没有大量计算工作的情况下推导Kerr解决方案。 （通常涉及计算机辅助符号代数。）也许在这方面最接近的是Newman-Janis Trick；一个技巧，需要几种身体上没有动力才能工作。在本文中，我们将尝试通过使用基于扁平的球体坐标来吸收尽可能多的凌乱的角度依赖性，从而在此问题上取得一些进展，从而吸收一个相对简单的角度独立的四型四组分指标。也就是说，我们将编写$ g_ {ab} = g_ {ab} \; e^a {} _ a \; E^b {} _ b $寻求保持tetrad-compongont $ g_ {ab} $和非正常型co-Tetrad $ e^a {} _ a $相对简单但非平凡。 We shall see that it is possible to put all the mass dependence into $g_{AB}$, while the non-ortho-normal co-tetrad $e^A{}_a$ can be chosen to be a mass-independent representation of flat Minkowski space in oblate spheroidal coordinates: $(g_\mathrm{Minkowski})_{ab} = η_{ab} \; e^a {} _ a \; e^b {} _ b $。该过程在很大程度上将质量依赖与旋转依赖性分开，并使Kerr解决方案也许有些神秘。
Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr solution without significant computational effort. (Typically involving computer-aided symbolic algebra.) Perhaps the closest one gets in this regard is the Newman-Janis trick; a trick which requires several physically unmotivated choices in order to work. Herein we shall try to make some progress on this issue by using a non-ortho-normal tetrad based on oblate spheroidal coordinates to absorb as much of the messy angular dependence as possible, leaving one to deal with a relatively simple angle-independent tetrad-component metric. That is, we shall write $g_{ab} = g_{AB} \; e^A{}_a\; e^B{}_b$ seeking to keep both the tetrad-component metric $g_{AB}$ and the non-ortho-normal co-tetrad $e^A{}_a$ relatively simple but non-trivial. We shall see that it is possible to put all the mass dependence into $g_{AB}$, while the non-ortho-normal co-tetrad $e^A{}_a$ can be chosen to be a mass-independent representation of flat Minkowski space in oblate spheroidal coordinates: $(g_\mathrm{Minkowski})_{ab} = η_{AB} \; e^A{}_a\; e^B{}_b$. This procedure separates out, to the greatest extent possible, the mass dependence from the rotational dependence, and makes the Kerr solution perhaps a little less mysterious.
