  A general formula is calculated for the connection of a central metric
w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using
the framework of linear connections on central bi-modules. The general formula
is further on used to calculate the corresponding Riemann tensor and prove the
corresponding Bianchi identities and certain symmetries that are essential to
obtain a symmetric and divergenceless Einstein Tensor. In particular, the
obtained Einstein Tensor is not equivalent to the sum of the noncommutative
Riemann tensor and scalar, as in the commutative case, but in addition a
traceless term appears.
