Question

Question A3 a) With respect to the spacetime line element ds2, what distinguishes trajectories classified as time- like, null or spacelike? Which type of trajectory must a massive particle follow? b) Why do we need the covariant derivative? Write down the covariant derivative acting on a cov- ector field. What is the covariant derivative of the metric?

Answer 1

ds²=0 ds² co ds? >0 light like time like space like - massive particle move along time like grodesics я). В сом А., а зам, дрос. - fut {as non zero curvature in this we don't have straight lines as one geodesics to take the affect of Curvature on geodesics, we need covariant derivatie en DEASE ONAR + Tus AB Covariant derivature - Du gur = o Covariaut derivative derivative of of metnic is zero metr