Hi Steve!
I thought you would like it. It tickles me every time I try to wrap my head around it. You can see that while a sphere's volume varies by a factor of 2 its volume varies by a factor of 8, so that's a linear function, but the exponential deceleration compounding density is nonlinear. The amount of energy required to constitute the density gets progressively less and less in ever smaller volumes as the density compounds exponentially, so a huge density value needs a minuscule amount of actual energy to be extremely effective. But the corker is that energy quantity is the hidden variable! Its there! but only expressed in the quotient and divisor; density = erg/cm^3. Energy quantity, is the dividend and only expressed as a non-dimensional point density value. (aarghh! Where is IT!) Its there, its about energy. But its total quantity is expressed through density. Like in GR, force is the hidden variable as the product, and expressed in the multiplier and multiplicand mass*acceleration.
It can be done (and was) geometrically and algebraically in Euclidean R4 space and time, but winds up forcing the issue of relativistic time dilation. It's not difficult to accept that energy with condense by slowing to rest from light velocity... sure. But then comes the ontological twist of once you are out there on the edge where energy is at an empirical minimum density at light speed... where can it go without sucking the energy out of the field? So the model forces acceptance that light velocity is the limit of speed of time, just like in SR. If time is going at light velocity, then the inertially bound enregy needs not move in space. Rather it cannot go any further than its zero boundary of minimum density, and saves space for the over abundance of energy in the universe. And in context with previous posts, the continuously connected energy in a quantum level field equates higher density with lower temperature, while in the general gravitational referrence higher density equates with higher temperature as a function of random particle motion. Kind of nice given todays announcement of the first real photograph of a black hole, where extreme density quiets particle motion down to the quantum level of high density and colder temperature.
What a nice day! jrc