You can argue it 3 ways. Black holes can go other universes, other points in our universe or nowhere. Experimental evidence for them going to points in our universe is low as we can see lots of black holes but no 'white holes'. Though all 3 are possible.
An infinite cylinder can be described by a continuous function of two variables and it has 0 curvature everywhere. P(a,z)=[cos(a),sin(a),z] is one possible function. I know that it needs to be normalized but continuty will be preserved.
Those are called "wormholes" or "Einstein-Rosen bridges." They're purely hypothetical; there is no evidence that suggests they actually exist. Einstein's theory of gravitation shows that space is curved near massive objects. To use the "flat sheet" analogy again, imagine space as a flat matress. If you put a heavy bowling ball on the matress (or a star in the universe), the space around it sags. Now you could theoretically get a less massive object such as a marble (a planet) to "orbit" the bowling ball (star). Einstein and Rosen's concept of a "bridge" connecting two universes or two regions of space-time comes from the fact that a supermassive object such as a black hole could cause the "matress" to sag so much that it "breaks" the space around the supermassive object. No one knows the laws of physics at a singularity, so it's hard to say if it leads to another point in space-time. I highly doubt it would be possible for any kind of living being or spacecraft to travel through a wormhole, and pop out somewhere else unharmed. Anything entering a wormhole will almost certainly be ripped to elementary particles by the tidal forces.
forgive me for my many questions but... If gravity is the bending of space-time around matter like the sun, and planets rotate the largest mass, why doesnt the earth spiral into the sun? I guess im picturing those funnel things that they have at science museums where u put a coin in and it rolls around and around until in falls into the center. What keeps the earth and other planets from "sliding" into the sun? Oh this is a two parter, second part is a bit off topic. Why does a planet like Pluto continue to rotate the sun when it a) is the furthest away b) has a large planet such as Uranus in front of it? That is, why doesnt Pluto fall into the orbits of either Neptune or Uranus instead of the Sun's when it is so far away?
The Earth doesn't fall into the Sun for the same reason that satellites continue to circle the world - the velocity overcomes the gravitational pull. Some say that Pluto is a remant of a solar system collision - that it originally was a moon of Saturn and that a passing rogue planet threw off one of Saturn's moons, and may have also caused the rings of Saturn and the Van Allen astroid belt. Who knows for sure? Either way Pluto's orbit is not circular - it is elliptical. We have hundreds, if not thousands, of satellites orbiting the Earth. Why don't they all crash into each other? http://www.nineplanets.org/ Now about your original question - Think of all the atoms and molecules in your body as the Universe. You see your skin - it is the boundary of the Universe. But X-Rays, Ultra Violet, Infra Red and Gamma Rays can get in. Likewise you release heat, light, electricity and gravity (along with love, hatred and lust). Now imagine that you are one atom with consciousness that travels through your body. When it passes your skin layer out into the world - what will it see and sense? The problem with 'singularity points' and a 'flat' Universe is one of perspective. Within that flat layer there is thickness, no matter how infinitisimal you may imagine it. Does it really make any difference if the whole Universe was as big as a bowling ball or the head of a pin? Without a relative point reference size doesn't matter. You have consciousnes. You dream in your brain. A nerve cell fires, you have a dream. Are you aware of the size of the Universe within your own mind while dreaming? Where is your sense of space and time? You only sense it while in the dream. While you are dreaming there is no time and same, there is no consciousness; it all looks black, unbounded, and infinite.
ok, point taken, although i dont appreciate doing maths on a sunday. Not for any religious reason but for the same reason I dont appreciate it the other 6 days
The earth is falling into the sun, very very slowly. The earth angular momentum is getting slightly smaller each year, given enough revolutions it will fall into the sun. However the solar system will disappear long before that happens.
the sun will turn into a black dwarf (a giant lump of charcoal). However first it will expand and engulf the inner planets up to Earth and possible mars also.
They grow. A back hole is not a singularity as defined before, it is simply something whos gravitational attraction is too strong for light to escape. The minimum size and object of a certain mass has to be to class as a black hole is called the Schwarzchild radius. For the Earth this is 9cm or 9m, i seem to remember from an exercise years ago.
Well...it doesn't NECESSARILY have a singularity if it is rotating very fast, but singularities probably exist in most black holes.