I've been thinking recently that for static systems (it won't work in general), you can treat gravity as being a two-form if you use the scaled "force at infinity" rather than the locally measured gravitational force. The "local force of gravity" is the acceleration of a worldline of a stationary observer (as measured by an accelerometer at the observer's worldline). The "force at infinity" is the "local force" multiplied by the time dilation factor between the observer's local clock and a clock at infinity. I was wondering if this tensor had a name, or if there were any papers exploring this analogy. It's more or less hinted at in Wald, where he mentions that you can integrate the "force at infinity" around a sphere to get the enclosed Komar mass, but he doesn't actually define the corresponding two-form |f@inf_a u_b|, where f@inf is the "force at infinity" or give it a name.