Recent content by rezkyputra

All in all, said tensor ##X^{AB}## in my post was actually an Energy momentum tensor, which should have a covariant derivative of zero ##\nabla_A X^{AB} = \nabla_A T^{AB} = 0 ## or is there a special case where that would be zero?

Homework Statement Suppose we have a covariant derivative of covariant derivative of a scalar field. My lecturer said that it should be equal to zero. but I seem to not get it Homework Equations Suppose we have $$X^{AB} = \nabla^A \phi \nabla^B \phi - \frac{1}{2} g^{AB} \nabla_C \phi \nabla^C...

Okay, it was a typo, i got it correct indices on my notes so let me retype it \begin{align} \delta \Gamma_{ab}^d &= \frac{1}{2} \left( - g_{qb} \, \nabla_a \, \delta g^{dq} - g_{qa} \, \nabla_b \, \delta g^{dq} + g_{ra} \, g_{sb} \, \nabla^d \, \delta g^{rs} \right) \nonumber \\...

Homework Statement Okay, in Carrol's Intro to Spacetime and Geometry, Chapter 4, Eq. 4.63 to 4.65 require a derivation of a difference between Christoffel Symbol. I did the calculation and found my answer to be somewhat correct in form, but the indices doesn't match up Homework Equations So...

Homework Statement It is shown in Carrol, an Introduction to GR that the variatiom of Christoffel symbols are : https://scontent-sin1-1.xx.fbcdn.net/v/t34.0-12/13535871_1161725257182772_897443562_n.jpg?oh=df1a6d26aa0b199d4684b5f0785bee20&oe=576ECCCA But i have no idea how to derive that, any...