Proof for the Weak and the Strong Energy Conditions Theorems in Einstein–Yang–Mills Theories

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.