>>12355003Yes there is to an extent. Quite a few things in gravity which naively should go as volume actually go as area. For example, the Hamiltonian of gravity is always a boundary term (and only in a theory of gravity this is so, see Regge-Teitelboim), not a volume term. This in a certain sense, is a restatement of Gauss law.
Another way to build up intuition is via exact holographic dualities like ads-cft. The entire theory of quantum gravity + corrections in the bulk is virtually dual to a quantum theory living on the boundary.
Recently some people are arguing whether holography is inbuilt in canonical gravity itself, in ads as well as in flat space. This means whether you can deduce about all the information deep in the bulk just from a small patch near the timelike infinity in ads or near the future null infinity in the flat space, without ever talking about the dual holographic description. This follows from the fact that in gravity, the existence of Gauss law demands that the Hilbert space doesn't factorise, and consequently you can construct operators describing a region, say in the interior of a black hole from the exterior itself. My personal opinion is that things like Gauss law have a lot more to say, that is presently understood.
In short, it should not come as a surprise if things go as area in gravity because of the above (and many other similar) reasons.
