 (Wald 1984, pg 158, problem 4)

formula_12
formula_13

We will demonstrate that integrating the normal component of the "acceleration at infinity" ainf over a bounding surface will give us a quantity that does not depend on the shape of the enclosing sphere, so that we can calculate the mass enclosed by a sphere by the integral

formula_14

To make this demonstration, we need to express this surface integral as a volume integral.In flat space-time, we would use Stokes theorem and integrate formula_15 over the volume.In curved space-time, this approach needs to be modified slightly.