This is to outline & detail a possible alternative to the illogical 'dark matter' hypothesis,
at least in so far as it concerns the particulars within each galaxy.
Non-Perpendicular Gravity Axis Theory:
Scale down space-time to a single sheet of rubber which is warped/pulled 'downward' as the curvature of gravity.
(This is the time-speed dimension.)
Since we know space-time is curved we know that locally perpendicular gravity axes can not all be parallel (they point different directions).
My theory takes this one step further & proposes that gravity axes may not even always be locally perpendicular,
that they may be locally non-perpendicular.
I speculate that the outer stars of the/a galaxy have the 'bottom' of their gravity axes (the stellar centers) drawn inward, namely towards the event horizon of the central black hole of any given galaxy.
I additionally pose that the inner stars of a given galaxy have the 'top' of their gravity axes drawn inward towards the central black hole.
This would mean that the outer stars have, on average, a gravity axis that is at an acute angle to the space-time between them and the central black hole of their galaxy.
The inner stars would have, on average, a gravity axis that is at an obtuse angle to the space-time between them & the central black hole of their galaxy.
This, i speculate, would mean the outer stars gravity, due to the acute angle, is additive to the gravity towards the central black hole.
The inner stars would, due to the obtuse angle, have a subtractive effect from the gravity towards the central black hole.
Now one must wonder why these non-perpendicularities occur.
We know that the rotation of objects creates a space-time 'drag' effect.
It seems easy to me to imagine that a central black hole that is thought to curve to infinity must be pulling all
the space ('nearby') around it into itself. This seems like it would likely pull the entire 'top' of the gravity form around inner (axes) stars towards it.
While those stars have not actually changed position in the higher dimensional space the curvature of their gravity has.
Now i need to address the more challenging explanation for the reason the outer stars (actually all the stars) have the bottom of their gravity axes pulled/drawn towards the event horizon of the central black hole.
In the interior of stars photons are created that are entangled with other central stellar elements.
Eventually these radiate outward from the star in all directions.
Over time a good portion of these arrive at the event horizon of the central black hole.
While many of these entangled photons decohere (lose their entanglement), the ones that arrive at the black hole's event horizon are slowed, almost stopped, in time, to a reasonable degree 'locking' them into a coherent (superposition) state with elements of a given star's interior, at least on their particular parameter of entanglement. Quantum tunneling is an event of decoherence, but these photons instead remain in a superposition state which sustains spatial/location ambiguity. The superposition is in the center of the star as well as at/on the event horizon of the central black hole.
All the stars have this occuring, but for the outer stars, being so much further from the center of the galaxy, this produces a much more pronouced effect. It produces a more sharply acute angle.
My thought is with non-perpendicular gravity axes, most especially the ones around objects that rotate, it would cause local rotating space to be flexing back & forth through different angles.
I think space-time may resist the constant flexing and tends to 'even' out (re-perpendicularize) the angular position locally.
Which imposes a local perpendicularity, but in local space that is at a different angle to the broad orientation of the space-time average.
This creates wrinkles in space-time, which means there is more space required than in flat (regions of) space.
If this compounded speculation is true it may produce some unusual gravity effects on the inner side of the far outer stars' gravity wells. It might even rise somewhat above the average flatter plane in the time-speed dimension. This might create some reverse gravity where distances are increased & time is sped up. Matter would tend to avoid, exit, go around these longer curving regions.
So that would be something to look for, matter avoiding, bypassing, circumnavigating on the inner side of outer galactic stars' gravity fields probably at some range of radii from each star.
This might make stable orbits more difficult to acheive, so perhaps a galaxy's outermost stars have very few planets that manage to stay in a reasonably stable orbits.
Thoughts:
Possibly observable effects,
1) With the inner stars, at least the ones between us and the central black hole, we may be 'seeing' them differently than they actually are if measuring directly from a star to the central black hole.
The distance from our viewpoint to an inner galactic star & then from that star to the central black hole is a longer distance than the distance directly from our viewpoint to the central black hole.
Use the '2' shape to think about it. We see the light from a star over the curve of the top of the '2' and when that is subtracted from our distance to the central black hole they may be calculated as apparently closer to the black hole than if one measured directly from the star across/through the flat bottom of the '2' to the central black hole.
It may be that on randomized average that the stars immediately on the far side of the central black hole from us 'seem' further away than the stars more directly between us and the central black hole.
2) A second thing to think about, is nacent young stars would have to wait until their initial entangled photons actually reach the central black hole, possibly a hundred thousand years, for this effect to even begin to take hold.
It might be possible to observe young outer galactic stars that seem less drawn towards the galactic center, which might give them some tendency to wander outward as a galaxy rotates, until they finally begin to demonstrate this additive gravity influence.
All of this is to attempt to explain the unexpected orbital speeds of stars in the vast majority of galaxies we can observe.
This would not account for any other non-uniform distributions of gravity that can not be accounted for by visible matter.
at least in so far as it concerns the particulars within each galaxy.
Non-Perpendicular Gravity Axis Theory:
Scale down space-time to a single sheet of rubber which is warped/pulled 'downward' as the curvature of gravity.
(This is the time-speed dimension.)
Since we know space-time is curved we know that locally perpendicular gravity axes can not all be parallel (they point different directions).
My theory takes this one step further & proposes that gravity axes may not even always be locally perpendicular,
that they may be locally non-perpendicular.
I speculate that the outer stars of the/a galaxy have the 'bottom' of their gravity axes (the stellar centers) drawn inward, namely towards the event horizon of the central black hole of any given galaxy.
I additionally pose that the inner stars of a given galaxy have the 'top' of their gravity axes drawn inward towards the central black hole.
This would mean that the outer stars have, on average, a gravity axis that is at an acute angle to the space-time between them and the central black hole of their galaxy.
The inner stars would have, on average, a gravity axis that is at an obtuse angle to the space-time between them & the central black hole of their galaxy.
This, i speculate, would mean the outer stars gravity, due to the acute angle, is additive to the gravity towards the central black hole.
The inner stars would, due to the obtuse angle, have a subtractive effect from the gravity towards the central black hole.
Now one must wonder why these non-perpendicularities occur.
We know that the rotation of objects creates a space-time 'drag' effect.
It seems easy to me to imagine that a central black hole that is thought to curve to infinity must be pulling all
the space ('nearby') around it into itself. This seems like it would likely pull the entire 'top' of the gravity form around inner (axes) stars towards it.
While those stars have not actually changed position in the higher dimensional space the curvature of their gravity has.
Now i need to address the more challenging explanation for the reason the outer stars (actually all the stars) have the bottom of their gravity axes pulled/drawn towards the event horizon of the central black hole.
In the interior of stars photons are created that are entangled with other central stellar elements.
Eventually these radiate outward from the star in all directions.
Over time a good portion of these arrive at the event horizon of the central black hole.
While many of these entangled photons decohere (lose their entanglement), the ones that arrive at the black hole's event horizon are slowed, almost stopped, in time, to a reasonable degree 'locking' them into a coherent (superposition) state with elements of a given star's interior, at least on their particular parameter of entanglement. Quantum tunneling is an event of decoherence, but these photons instead remain in a superposition state which sustains spatial/location ambiguity. The superposition is in the center of the star as well as at/on the event horizon of the central black hole.
All the stars have this occuring, but for the outer stars, being so much further from the center of the galaxy, this produces a much more pronouced effect. It produces a more sharply acute angle.
My thought is with non-perpendicular gravity axes, most especially the ones around objects that rotate, it would cause local rotating space to be flexing back & forth through different angles.
I think space-time may resist the constant flexing and tends to 'even' out (re-perpendicularize) the angular position locally.
Which imposes a local perpendicularity, but in local space that is at a different angle to the broad orientation of the space-time average.
This creates wrinkles in space-time, which means there is more space required than in flat (regions of) space.
If this compounded speculation is true it may produce some unusual gravity effects on the inner side of the far outer stars' gravity wells. It might even rise somewhat above the average flatter plane in the time-speed dimension. This might create some reverse gravity where distances are increased & time is sped up. Matter would tend to avoid, exit, go around these longer curving regions.
So that would be something to look for, matter avoiding, bypassing, circumnavigating on the inner side of outer galactic stars' gravity fields probably at some range of radii from each star.
This might make stable orbits more difficult to acheive, so perhaps a galaxy's outermost stars have very few planets that manage to stay in a reasonably stable orbits.
Thoughts:
Possibly observable effects,
1) With the inner stars, at least the ones between us and the central black hole, we may be 'seeing' them differently than they actually are if measuring directly from a star to the central black hole.
The distance from our viewpoint to an inner galactic star & then from that star to the central black hole is a longer distance than the distance directly from our viewpoint to the central black hole.
Use the '2' shape to think about it. We see the light from a star over the curve of the top of the '2' and when that is subtracted from our distance to the central black hole they may be calculated as apparently closer to the black hole than if one measured directly from the star across/through the flat bottom of the '2' to the central black hole.
It may be that on randomized average that the stars immediately on the far side of the central black hole from us 'seem' further away than the stars more directly between us and the central black hole.
2) A second thing to think about, is nacent young stars would have to wait until their initial entangled photons actually reach the central black hole, possibly a hundred thousand years, for this effect to even begin to take hold.
It might be possible to observe young outer galactic stars that seem less drawn towards the galactic center, which might give them some tendency to wander outward as a galaxy rotates, until they finally begin to demonstrate this additive gravity influence.
All of this is to attempt to explain the unexpected orbital speeds of stars in the vast majority of galaxies we can observe.
This would not account for any other non-uniform distributions of gravity that can not be accounted for by visible matter.