One of my professors wrote on the board
(1) Mass tells spacetime how to curve $\to$ Metric/Einstein Field Equations
(2) Spacetime tells mass how to move $\to$ Geodesic equation
Suppose I am given the following metric:
$$ds^2 = -c^2dt^2 + dl^2 + (k^2 +l^2)(d\theta^2+\sin^2\theta d\phi^2)$$
Given this metric, do I have enough information to get useful information from
(1) the Einstein Field Equations
(2) the geodesic equation
In other words, besides the metric, how many other pieces of information do I need before I can set up the Einstein Field Equations and the geodesic equation and start extracting information about how test particles will behave in this space?
Apologies for any abuse of terminology. I am just learning this stuff, so please correct me if I didn't state the question well.