I am a newbie in the field of general relativity. Recently my prof shared a paper with me which talked about solving differential equations with some novel method. He asked me to solve Einstein equation to obtain a black hole solution. However, seeing the form of einstein equations, i cannot see how will they form a system of differential equations. My model is built for system of ODEs. I can plug any number of ODEs and it will give me the solution.
Could you please help me visualise this on how can i obtain a system of differential equations from this einstein equation and how will they look like. Will the system be ordinary or would it be partial DEs. Because right now my model is built for system of ODEs. Is there any way i can plug these in my system to obtain the desired solution.