Abstract

We present the manifest proof of the validity of the local weak and strong energy conditions in all Einstein–Maxwell–Yang–Mills space-times where nonnull electromagnetic and Yang–Mills fields are present. To this end, we make use of the new tetrads introduced previously. These new tetrads have remarkable properties in curved four-dimensional Lorentzian space-times. For example, they diagonalize locally and covariantly any stress-energy tensor in Einstein–Maxwell space-times and also in Einstein–Maxwell–Yang–Mills space-times for nonnull electromagnetic and Yang–Mills fields. We use these properties in order to prove the energy conditions for any space-time with these characteristics.

中文翻译：

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爱因斯坦-杨-米尔斯理论中弱和强能量条件定理的证明

摘要

我们提出了在存在非零电磁场和杨米尔斯场的所有爱因斯坦-麦克斯韦-杨-米尔斯时空中局部弱和强能量条件的有效性的明显证据。为此，我们利用之前介绍的新四分体。这些新的四分体在弯曲的四维洛伦兹时空中具有显着的特性。例如，它们对爱因斯坦-麦克斯韦时空以及非零电磁场和杨-米尔斯场的爱因斯坦-麦克斯韦-杨-米尔斯时空中的任何应力-能量张量进行局部和协变对角化。我们利用这些性质来证明具有这些特征的任何时空的能量条件。