[puppypower (OP)]

Say we started with an object with a given amount of rest mass. Next, we add more and more rest mass to the object. According to GR and observations, space-time will contract and the internal pressure of the object will increase.

On the other hand, if we started with the same object of initial rest mass, and increased its velocity to generate the equivalent amount of relativistic mass; SR, space-time will contract, but the pressure does not increase. This suggests that rest mass and/or relativistic mass might be the foundation for changes in space-time.

Changes in energy wavelength (E=MC2), such as a red shift, does not alter space-time.  However, energy can generate pressure on matter.

The observation that any amount of rest mass at velocity V will show the same space-time contraction suggests the space-time induction by mass happens at the smallest unit of mass, so it is always in proportional to velocity and not bulk rest mass.

The next question does dark matter act more like rest mass or relativistic mass?

[jeffreyH]

Let us just for fun imagine a light second measuring stick marked off in light second intervals. Let us also imagine this measuring stick to be at rest with respect to an object moving parallel to it at relativistic speed with a gamma factor of 2. This means that time is dilated so that in the moving frame one second takes two seconds to pass when calculated from the rest frame of the measuring stick. Also two intervals on the stick will contract to the size of one when observed from the moving frame. In the rest frame of the measuring stick no such contraction can ever be observed.

You need to take this into consideration.