Geometrization conditions for perfect fluids, scalar fields, and electromagnetic fields
Geometrization conditions for perfect fluids, scalar fields, and electromagnetic fields
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完美流体、标量场和电磁场的几何化条件
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Charles G. Torre
中科院分区：
文献类型：
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作者：
Dionisios Krongos;Charles G. Torre
回顾并扩展了广义相对论中物质场时空“几何化”的rainich型条件。考虑了三种类型的物质：完美流体、标量场和电磁场。给出了时空度规成为爱因斯坦方程的完美流体解的一部分的充分必要条件。得到了由度规构造流体的公式。所有流体结果适用于任何时空维度。在度规上定义爱因斯坦标量场方程的解和从度规构造标量场的公式所必需和充分的几何条件是统一的，并扩展到任意维度，包括宇宙常数，并包括任何自相互作用势。给出了四维时空度规是电真空的充分必要条件，并推广了由度规构造电磁场的公式，使之包含了一个c…
Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equations are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Geometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and formulas for constructing the scalar field from the metric are unified and extended to arbitrary dimensions, to include a cosmological constant, and to include any self-interaction potential. Necessary and sufficient conditions on a four-dimensional spacetime metric for it to be an electrovacuum and formulas for constructing the electromagnetic field from the metric are generalized to include a c...