In the
first two articles in this series, we looked at the Einstein Field Equation and Maxwell’s Equations in a static, spherically symmetric spacetime. Using formulas from those two previous articles, I now want to consider the question: what is the maximum amount of work that can be extracted by slowly lowering an object into a static, spherically symmetric gravitational field? This is a concrete, physical way of defining the concept of “potential energy”. (We’ll come back to the concept of “potential energy” and its relationship to other concepts of energy at the end of this article.)
We start with some comments and definitions. By “slowly lowering” we mean that the radial motion of the object is at some very slow, constant speed so that we...