Hawking–Ellis type III spacetime geometry
Hawking–Ellis type III spacetime geometry
复制标题
霍金-埃利斯 III 型时空几何
DOI：
10.1088/1361-6382/aad473
复制
发表时间：
2018
影响因子：
3.5
通讯作者：
M. Visser
中科院分区：
文献类型：
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作者：
P. Martín;M. Visser
霍金-埃利斯(Segre-Plebański)分类中的III型(以及“本质核”III0)应力-能量张量的突出之处在于，到目前为止还没有已知源(经典或半经典)导致III型应力-能量。(相比之下，霍金-埃利斯第一类和第二类是经典的，而第四类是已知的半经典的)。相反，我们从反面的问题开始：什么样的时空(假设爱因斯坦方程)需要III型应力能量来支持它？一个关键的观察是，类型III与平面或球对称都不兼容，所以人们应该观察对称性较低(或没有对称性)的时空。要找到这样的III型时空，需要设法找到度规的适当ansatz，计算爱因斯坦张量，并分析(Lorentz不变)特征值和特征向量的模式。在这里，我们报告了沿着这些路线取得的一些(部分)成功--我们明确地展示了几个(有些不自然的)具有III型爱因斯坦张量的时空几何。然后，我们建立了一个显式但有点奇怪的拉格朗日模型，导致(在Minkowski空间中)第三类应力-能量。虽然我们仍然没有完全可以接受的III型应力能量的通用物理模型，但我们至少可以说一下这样的应力能量张量将带来什么。
The type III (and the ‘essential core’ type III0) stress-energy tensors in the Hawking–Ellis (Segre–Plebański) classification stand out in that there is to date no known source (either classical or semi-classical) leading to type III stress-energy. (In contrast the Hawking–Ellis types I and II occur classically, and type IV is known to occur semi-classically). We instead start by asking the obverse question: what sort of spacetime (assuming the Einstein equations) needs a type III stress-energy to support it? One key observation is that type III is incompatible with either planar or spherical symmetry, so one should be looking at spacetimes of low symmetry (or no symmetry). Finding such a type III spacetime is a matter of somehow finding an appropriate ansatz for the metric, calculating the Einstein tensor, and analyzing the pattern of (Lorentz invariant) eigenvalues and eigenvectors. Herein we report some (partial) success along these lines—we explicitly exhibit several (somewhat unnatural) spacetime geometries with a type III Einstein tensor. We then build an explicit but somewhat odd Lagrangian model leading (in Minkowski space) to type III stress-energy. While we still have no fully acceptable general physical model for type III stress-energy, we can at least say something about what such a stress-energy tensor would entail.
DOI：
10.1017/9781009253161
发表时间：
2023-02
期刊：
--
影响因子：
--
作者：
S. Hawking;G. Ellis
通讯作者：
S. Hawking;G. Ellis