Curvature, as explained by most mathematical treatments, could be considered as a poor orphan stepchild from the large-scale interaction in the family of gravitational forces and matter. In the newer C-R theory concept, geometric curvature plays the only role in the overall behavior of gravity.
In his theory of Relativity, Einstein proposed that gravity was the result from the four dimensional interaction of a warped geometry and it's effect on real matter. He seemed to spend a large amount of time trying to relate that geometric concept to the other basic forces of nature, without success.
From the C-R theory, we have pursued [some, no doubt would say warped] this geometric concept exclusively. Briefly, the key to our idea is that gravity is an effect, not actually a cause. The cause of gravity is the curvature, i.e., bending, twisting, or warping of space. This curvature de-activates, or slows down the real time experienced by matter. The curvature, technically speaking, warps the resident energy packet through a longer, more distorted, more confined, less real-time-quickness, situation. In exchange for this loss of activity, measured in real-time, the particle gains kinetic energy, or speed.
If the particle gains sufficient speed, there will inevitably be collisions. From these interactions, the particle may lose some of it's kinetic energy in the form of photons of heat, light, or some other frequency of electromagnetic radiation.
Indirectly, the energy of the photons released by this collision process comes from the release of kinetic energy freed by the curvature of time. The amount of curvature encountered will entirely determine how much of the stored up energy is available to be released from a particle. We can suppose that, upon entry into a Black-Hole a particle will either have yielded it's entire available contents of energy, or will carry that energy burden around (and around, and around, ad nauseam...) until the confinement is over.
The energy released by any particle in a gravitational field could be said to result from the yielding (or exchange) of real-time activity by that particle, to a less energetic, more highly warped or convoluted spacetime. The particle would be seen by the outside world to have it's internal clock slowed down as it gained kinetic energy. This energy would equal the time-loss times the mass of the object times the speed of light squared. Since the time loss is directly proportional to the curvature, the rate of energy released is proportional to the warping, or curvature and the rate is independent of the mass.
We may suspect that curvature of spacetime, which results in the decrease of real-time in that vicinity, might be the cause of much, if not all, of the redshift detectable in the universe. Unfortunately, we are unable to formulate or predict a viable, short term scenario which can clearly or distinctly tell the difference at the present time, whether matter is receding from the center of the universe at speeds astoundingly close to light speed, or whether the observed redshift is gravitationally created. If the redshift observed was due to a combination of both (rapid) recession and gravitational curvature, then we might never be able to measure and to separate-out each contributing component. Each of these figures would be necessary to plug into a suitable formula to find out both how large the universe is, and how old it is.