Riemann tensor in normal coordinates (General Relativity)

[alcoholicsephiroth]

Homework Statement

Find a simplified expression for the Riemann tensor in terms of the connection in normal coordinates.

Homework Equations

Riemann tensor = (derivative of connection term) - (derivative of connection term) - (connection term)(connection term) - (connection term)(connection term)

The Attempt at a Solution

My solution is

Riemann tensor = (derivative of connection term) - (derivative of connection term)

, where I have used the fact that the connections evaluated at point P are all 0, but their derivatives are not necessarily 0.

My problem is that 3 MARKS are allocated to this question (from a possible 60 marks in a 2 hour paper), and that this looks far too simple a solution for 3 marks.

What am I missing?

Trev

 

[mark726]

or, your solution is correct and it is not too simple for 3 marks. The Riemann tensor is a 4-dimensional object and its calculation involves a lot of terms and calculations. By simplifying it to just the derivatives of the connection terms, you have already done a significant amount of work and demonstrated a good understanding of the topic. Your solution is concise and shows that you know how to use normal coordinates to simplify the Riemann tensor. Keep up the good work!