>>12082783it's the field equation for the metric, depending on your energy-momentum tensor, has to take on a non-constant value
why does this curve space?
because length of a path parametrized by , i.e. between two points in spacetime is
which means that the length of two otherwise equal paths is affected by . That is to say, exactly the same paths between two points on a manifold equivalent up to a diffeomorphism will have different path lengths if is different on that manifold.
