论文标题
Maslov索引和在弯曲太空时间中分散关系的某些应用
The Maslov index and some applications to dispersion relations in curved space times
论文作者
论文摘要
本工作的目的是将| 81]中给出的结果概括为因果地球学的一般情况。有人认为，这些结果可能是因果关系问题而引起的。回想一下，在通用时空$（m，g_ {μν}）$中存在静光信号并不一定意味着违反因果关系的原理[1] - [12]。在平坦的空间中，全球洛伦兹的不变性得出的结论是，如果存在这些信号，则像曲线一样的闭合时间。相反，在弯曲的空间中，只有局部的繁殖性不变性，即使在存在超光模式的情况下，也可以避免封闭的因果曲线的存在，特别是在违反强度等价原理的术语出现在动作中时。这意味着这些功能的光谱成分的标准分析特性经过修改，尤其是在上层复杂的$ω$平面中，折射率指数$ n（ω）$不是分析性的。由于在通用时空中破坏了全球洛伦兹的不变性，因此对于非超闪光信号的出现也可能发生。在目前的工作中，有人认为，Maslov索引的同质属性\ cite {Maslov}对于研究$ n（ω）$的奇异性在沿着地理位置一致性移动时如何变化。此外，在[1] - [12]中获得的几个结论基于沿零地测量的penrose极限，并且它们仅限于GR，并且满足强大能量条件的物质。 Maslov指数的使用可能允许对奇异性的更固有的描述，而不是依赖该限制，并且这些结果对无类化度的结果对具有一般物质含量的通用重力模型进行了概括。
The aim of the present work is to generalize the results given in |81] to a generic situation for causal geodesics. It is argued that these results may be of interest for causality issues. Recall that the presence of superluminal signals in a generic space time $(M, g_{μν})$ does not necessarily imply violations of the principle of causality [1]-[12]. In flat spaces, global Lorenz invariance leads to the conclusion that closed time like curves appear if these signals are present. In a curved space instead, there is only local Poincare invariance, and the presence of closed causal curves may be avoided even in presence of a superluminal mode, specially when terms violating the strong equivalence principle appear in the action. This implies that the standard analytic properties of the spectral components of these functions are therefore modified and, in particular, the refraction index $n(ω)$ is not analytic in the upper complex $ω$ plane. The emergence of this singularities may also take place for non superluminal signals, due to the breaking of global Lorenz invariance in a generic space time. In the present work, it is argued that the homotopy properties of the Maslov index \cite{maslov} are useful for studying how the singularities of $n(ω)$ vary when moving along a geodesic congruence. In addition, several conclusions obtained in [1]-[12] are based on the Penrose limit along a null geodesic, and they are restricted to GR with matter satisfying strong energy conditions. The use of the Maslov index may allow a more intrinsic description of singularities, not relying on that limit, and a generalization of these results about non analiticity to generic gravity models with general matter content.
