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首页> 外文期刊>Electronic journal of theoretical physics >Relativistic Pentametric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold
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Relativistic Pentametric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold

机译：相对论本地化系统的相对论五坐标和时空流形的投影几何

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Relativistic pentametric coordinates supplied by relativistic auto-locatingpositioning systems made up of four satellites supplemented by a fifth one are defined inaddition to the well-known emission and reception coordinates. Such a constellation of fivesatellites defines a so-called relativistic localizing system. The determination of such systemsis motivated by the need to not only locate (within a grid) users utilizing receivers but, moregenerally, to localize any spacetime event. The angles measured on the celestial spheres of thefive satellites enter into the definition. Therefore, there are, up to scalings, intrinsic physicalcoordinates related to the underlying conformal structure of spacetime. Moreover, they indicatethat spacetime must be endowed everywhere with a local projective geometry characteristic ofa so-called generalized Cartan space locally modeled on four-dimensional, real projective space.The particular process of localization providing the relativistic pentametric coordinates is based,in a way, on an enhanced notion of parallax in space and time generalizing the usual parallaxrestricted to space only.
机译：除了众所周知的发射和接收坐标外，还定义了由相对论自动定位系统提供的相对论五坐标，该系统由四颗卫星组成，并辅以第五颗卫星。这样的五个卫星星座定义了所谓的相对论定位系统。确定这种系统的动机是，不仅需要利用接收器定位（在网格内）用户，而且通常需要定位任何时空事件。在五颗卫星的天球上测得的角度进入定义。因此，直到标度为止，都存在与时空的底层共形结构有关的内在物理坐标。此外，它们表明时空必须在任何地方都具有所谓的广义Cartan空间的局部投影几何特征，该局部Cartan空间是在四维真实投影空间上局部建模的。提供相对论五角坐标的特定定位过程在某种程度上是基于在空间和时间上增强了视差概念，将通常的视差仅局限于空间。

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