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The recent observations of the increasing expansion rate of the universe seem to indicate that we have a negative cosmological constant, which means, in the above discussions, that we have a saddle-shaped universe.
What does a negative cosmological constant imply in terms of physics? It means there is some uniform background of repulsive gravity everywhere. Now, this repulsive force is too small to be measured on any local scale so far, but when you consider larger and larger scales, this very small value begins to matter (no pun intended).
As far as some other observations in this thread, that somehow a black hole at the center of the galaxy means that we will someday be sucked in, albeit a long time in the future, this is not necessarily the case. Galaxies don't suck, nor do black holes. They simply accrete. There is fundamentally no difference between the earth orbiting the sun and the sun orbiting the center of our galaxy. It does not matter one whit whether the mass at the center is in the form of a black hole or just a bunch of stars. If our sun suddenly collapsed (it cannot do that), we would stay in our current orbit. We would not be suddenly sucked in. What determines our orbit is our current velocity, our mass and the mass of all matter in our neighborhood, but most particularly, that inside our orbit. (mass outside our orbit affects us primarily by perturbing our orbit. Even though the black hole at the center of our galaxy is gaining mass by accreting from nearby gas and stars, it still is not changing the total mass at the center of our galaxy, but merely rearranging it, so to speak. So, other than some possible perturbations in our orbit, but overall energy of the orbit is not really significantly affected.
One issue that would come up if our sun became a black hole is that the current solar winds would no longer be there, and so we would lose some small outward pressure on our orbit. However, this is small in comparison to the total energy of our orbit, so it would not amount to much. Of course, our planet slows down anytime it runs into anything (meteoroids, dust, etc.) and whenever those silly rocket scientists use us to slingshot some silly spacecraft, but we won't worry too much about that unless the spacecraft get really, really big. In the end, the earth will maintaim orbit long after the sun is no longer so useful to us.
So, what could cause our sun to move towards the center of our galaxy? Anything that decreased its velocity in orbit, which is the same as decreasing its energy in the orbit. Changing the direction of the orbit is pretty much the same thing, so I just include that here. How could this happen? Hitting dust clouds is one way, this could slow down the sun in its path. Another would be close encounters with other stars, which could just as easily put us on an orbit further out. However, nothing that happens at the center of our galaxy, in the neighborhood of our billions of years old black hole is likely to do much to change our orbit. You might consider that the matter falling into the black hole might even push us out a little bit because of the intense radiation given off as matter nears the horizon (due to collisions with other matter in the rapidly rotating accretion disc, for instance). Is this enough to counter the loss of outward pressure due to the radiation from the stars that are being or have been accreted? Probably not, but the overall determinining factor is more in the orbital mechanics than in the increase or decrease of radiation and particle pressure from the center. Again, losing the pressure does not suck us in, but simply doesnt' push us out as much.
Anyway, just some points about the black hole at the center of our galaxy and how it is no threat whatsoever to our continued existence. Our sun will cease to support life on earth long before the end of our galaxy by any means that we can forsee (no galactic collisions on the near horizon, etc.).
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