Energy Flow Near a Mass

The energy stress tensor in GR describes the density and flux of energy in a gravitational field. So what does the energy density gradient of the field look like near a mass? Flux describes flow, so I would guess the energy stress tensor describes (not only but including) the flow of energy in the gravitational field at any point. Where does the energy flow from and where to ? in the reference frame of a static mass, without other influence, is there zero energy flow? Do these questions even make sense?
- Andy Findlay (age 52)
Switzerland

I think your questions mostly make sense and can start to answer some. The idea of a "static" mass is of course non-relativistic, so here I think you mean a mass feeling no forces. That would be a mass "in free fall", following a geodetic path. It does not follow that the energy flow at that region is zero in the frame of the mass, because other forms of energy may feel forces, e.g. electrical forces, and they will not follow geodetics. Furthermore, other geodetics can intersect that one at some spacetime point. For example, say the mass is a little piece of glass and some light rays pass through it. In the frame of the glass, there's some energy flow. So you can see that all sorts of different energy flows are possible near that free-fall mass. 

Probably this only answers a fraction of what you were curious about. Follow up if you'd like us to find a colleague to answer more.

Mike W.

(published on 01/05/2016)