所有带有可预测、可解释和可量化物质的张量时空的引力动力学
Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable and quantizable matter
摘要：
只有严格限制的一类张量场才能提供经典的时空几何，也就是说，那些可以携带物质场方程的时空几何是可预测的、可解释的和可量化的。物质的这三个条件转化为张量几何的三个相应的代数条件，即双曲性、时间定向性和能量可区分性。作为广义相对论和粒子物理学的标准模型基础的洛伦兹度规，恰好给出了满足这些条件的最简单的张量时空几何。在本文中，对于满足上述最低要求的一般张量时空几何，引力动力学的求解问题被重新表述为一个线性偏微分方程组，因为它们的解产生了支配相应时空几何的作用。因此，对修正的引力动力学的研究就被简化为一项明确的数学任务。
英文摘要：
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics---for the general tensorial spacetime geometries satisfying the above minimum requirements---is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task.
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