As the metric tensor
Further, the Christoffel symbols are given as :
So, for example,
here, following Einstein's notation, the sum is over m. As the metric here is general, you have to calculate and write all the derivative terms separately. IN general, the terms will look like:
The list of terms is extremely long. Be careful.
Once you have the Christoffel symbols, to find the RIcci Tensor, you first calculate the RIemann Tensor which is obtained as:
The Ricci scalar is found by contracting the Ricci tensor with metric tensor once more: