The energy distribution is still the same from the core to the outer edges of the galaxy. If it wasn't, then it would collapse.
Inertial mass is a property of the space you are in. With a decreasing gravitational field, the inertial mass of an object decreases. The same velocity does not equal the same amount of energy. To maintain energy conservation, I tied the reduced gravitational field, to the faster flow of time. The flow of time is (nearly?) infinite in empty space. Binding the two together seems to work and appears to be consistent. A lower gravitational field equates to an increase in the flow of time, AND a lower inertial mass.
A partial analogy is to think how much energy an arrow would require to move through air or water.
A mass in motion, remains in motion. This is where the arrow analogy breaks down.
Imagine space as containing an infinite number of gravitational compass needles.
The needles have a very tiny mass, and like the magnetic compass needles, the gravitational compass needle has one side which is repelled by a gravitational field and one side which is attracted to a gravitational field.
It takes very little work to affect a small change in the randomness of the needles. But to make this work they need to have a preferred direction that they will return to.
A single mass will slightly deflect all the compasses within a volume of space, from their preferred orientation.
As the mass is accelerated through a space that contains these randomly pointing compasses, only a little bit of work is necessary to accelerate it and once at a velocity, to maintain its velocity.
How does the mass maintain velocity? The work that goes in to getting the mass up to velocity, was used to change the positions of a few needles from their preferred orientation. As the mass passes, the needle moves to its preferred position and brings its gravitationally repellent side to partially repel the mass.
As it moves at a fixed velocity, it is losing energy to the compass needles in front of it, while gaining an equal amount of energy from the compass needles behind it. A body in motion stays in motion.
Now lets add an ambient gravitational field. All of the random needle orientations are now slightly less random producing a local gravitational vector. The strength of the field is related to how much the needles diverge from randomness. Perfect alignment occurs at at g level greater than the acceleration of light.
With an ambient gravitational field present, it takes more energy to shift the needles. It takes more energy to get it up to the same velocity, then when the ambient field was not present. If the ambient gravitational is orienting a needle to oppose its movement, the object will need more energy to change the needles orientation because of the static gravitational field.
The inertial mass of the object has increased in the ambient gravitational field. The needles require more energy to change position. Once at a fixed velocity, it losses energy to the compass needles ahead of it and gains the same amount of energy from compass needles behind it.
Inertial mass is a property of the space an object mass moves through.
I bound time to the gravitational field by giving time (nearly?) infinite flow in empty (gravitationally free) space. Time slows down, with increasing gravitation.
Getting it from a concept or analogy to a mathematical construct is gonna be a challenge.
