# Alcubierre metric as an explanation for dark matter halos

• I
So I have a question regarding the Alcubierre metric and the phenomena of stars on outer edges of galaxies moving at higher velocities than their orbital calculations state they should. When taking the accelerating expansion of space into account due to dark energy, could a sub-luminal Alcubierre-like effect be a possible explanation for why these stars appear to move faster than they should?

Take a star at the outer edge of the galaxy moving in a straight line, which in a gravity well as I understand it, is in orbit.

The space in front of that star is contracted due to the gravity of the galaxies center and contracts further the closer you move towards the center. In the direction away from the galaxy, space is relaxing as the strength of gravity weakens. However, when you take expansion due to dark energy into account, that space that is in the direction away from the galaxy is also experiencing increased expansion, some effective negative mass due to dark energy expansion, just not enough to completely overcome gravity.

That seems similar to the description made for an Alcubierre field, where an area of space behind an object is expanding, while the area in front of it contracts. It's not exact, since the area of expansion and contraction aren't at 180 degree angles to the star, but in principle it seems similar.

So, could it be possible that, from the stars reference frame, it actually travels at the exact velocity it should be traveling to orbit the galaxy, but from the perspective of a distance observer it appears to be moving faster than it should?

Orodruin
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No. Gravitationally bound systems do not expand and the Alcubierre metric does not work as you imagine. Also, dark energy does not have negative energy density.

But from what I've read about dark energy, it's present in all space, which would include within galaxies. And it does cause space to expand, just not a rate that exceeds the force of gravity. I do have a laymans understanding of the Alcubierre metric, but it seems that the expansion of space is what allows the effect to occur, its just when producing one artificially, you'd need a negative energy density to create that expansion of space. But if space is expanding naturally, why can't the same effect occur at very large scales?

Orodruin
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Please provide references in accordance with PF rules.

And it does cause space to expand,
This is a misconception. Space would expand even if there was no dark energy. Dark energy causes accelerated expansion. That it is present in a galaxy does not mean that the gravitationally bound system will expand.

I am sorry, but it seems you are just speculating based on buzzwords from popular science. This is not a proper way of theorizing in science.

Please provide references in accordance with PF rules.

This is a misconception. Space would expand even if there was no dark energy. Dark energy causes accelerated expansion. That it is present in a galaxy does not mean that the gravitationally bound system will expand.

I am sorry, but it seems you are just speculating based on buzzwords from popular science. This is not a proper way of theorizing in science.

That's why I'm asking questions and not writing papers on astrology.

I'm not asking if the galaxy expands. My question is whether or not the accelerated expansion of space, due to dark energy, and the contraction of space, due to gravity around a star, could affect the perceived velocity of a star for a distant observer.

My references for the information are:
https://en.wikipedia.org/wiki/Dark_energy
https://en.wikipedia.org/wiki/Alcubierre_drive#Alcubierre_metric

Orodruin
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Well, based on your current level of understanding, the best answer would be a simple ”no”.

Well, based on your current level of understanding, the best answer would be a simple ”no”.

Ouch that's pretty harsh. I've read quite a few theories on the matter of dark energy and gravity. Can't say I've seen anyone provide the definitive understanding of these particular phenomena yet.

PeterDonis
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My question is whether or not the accelerated expansion of space, due to dark energy, and the contraction of space, due to gravity around a star, could affect the perceived velocity of a star for a distant observer.

First, gravity around a star does not make space contract.

Second, while it is true that the velocity of an object in a gravity well (of a star or a galaxy or any massive object) as seen by observers nearby, will be different from the velocity as seen by observers very far away, the magnitude of this effect for galaxies is much too small to account for the features of galaxy rotation curves that dark matter is hypothesized to explain.

Third, expansion of space, accelerated or not, affects all observations that we see from a distant galaxy equally, so it cannot account for the rotation curves of a galaxy being different from what is expected from their visible matter content; such an effect would require light from different parts of the galaxy to be affected differently as it travels from the distant galaxy to us, which is not what expansion of space does.

mfb
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That's why I'm asking questions and not writing papers on astrology.
Astronomy, not astrology.

You are asking questions of the type "Does B follow from A?" - where A is wrong.
Can't say I've seen anyone provide the definitive understanding of these particular phenomena yet.
We have models consistent with observations. That is not a "definitive understanding", but it is a very high bar for new models. They have to get all these things right as well to compete. Galaxy rotation curves, all the tests of general relativity in the solar system, around neutron stars and black holes, lensing from stars to galaxy clusters, star cluster velocities, velocity distributions of whole galaxies in groups, spatial resolved gravitational lensing from galaxies, supernova data for the expansion, the formation of galaxies and their distribution, all evidence for dark matter and dark energy in the cosmic microwave background, ...