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Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

机译:一类模型中瞬时3-空间的动态出现 广义相对论

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摘要

The Hamiltonian structure of General Relativity (GR), for both metric andtetrad gravity in a definite continuous family of space-times, is fullyexploited in order to show that: i) the "Hole Argument" can be bypassed bymeans of a specific "physical individuation" of point-events of the space-timemanifold $M^4$ in terms of the "autonomous degrees of freedom" of the vacuumgravitational field ("Dirac observables"), while the "Leibniz equivalence" isreduced to differences in the "non-inertial appearances" (connected to "gauge"variables) of the same phenomena. ii) the chrono-geometric structure of asolution of Einstein equations for given, gauge-fixed, initial data (a"3-geometry" satisfying the relevant constraints on the Cauchy surface), can beinterpreted as an "unfolding" in mathematical global time of a sequence of"achronal 3-spaces" characterized by "dynamically determined conventions" aboutdistant simultaneity. This result stands out as an important "conceptualdifference" with respect to the standard chrono-geometrical view of SpecialRelativity (SR) and allows, in a specific sense, for an "endurantist"interpretations of ordinary "physical objects" in GR.
机译:为了明确地表明:在一定的连续时空族中,公制和四重重力的哈密顿广义相对论(GR)结构都得到充分利用,以表明:以真空引力场的“自主自由度”(“狄拉克可观察物”)表示的时空流形$ M ^ 4 $的点事件,而“莱布尼兹当量”归结为“非自由度”的差异。相同现象的“惯性出现”(连接到“量规”变量)。 ii)对于给定的,经轨距固定的初始数据(满足柯西曲面的相关约束的“ 3-几何”),爱因斯坦方程解的时间几何结构可以解释为数学上的全局时间“展开”一系列“异步3-空间”,其特征是关于遥远同时性的“动态确定的约定”。就标准相对论(SR)的时空几何学观点而言,这一结果是一个重要的“概念差异”,并且在特定意义上允许对GR中的普通“物理对象”进行“耐力主义”解释。

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