Re: I would like a function for a vortex please.

Question: I would like a function for a vortex please.

I am chasing a function for a vortex, for use in a singularity (black hole) simulation. I would like to be able to pick the exact point in the vortex that a certain object may be. I wish to adapt this function to include mass of object, linear direction, linear angle, velocity, and other variables that may help in calculating other things such as escape velocity for that particular function. I would appreciate any help, even links to similar research.

Black holes are tricky. To completely answer your question would require a semester course in General Relativity (GR). There are excellent lecture notes on the subject that will take you through GR, so in my answer I'll just try to describe why the problem is so difficult.

The idea of black holes was first proposed by John Mitchell in the 1800's, and he was using Newton's Law of Universal Gravitation. Put simply, if enough mass could be compressed into a small enough space, the gravitational pull would be great enough that nothing, not even light, could escape.

With Newtonian gravity, a body will orbit a black hole in exactly the same fashion that an object orbits the sun: the path will either be a parabola, hyperbola, or an ellipse depending on the initial velocity of the object.

But Newtonian gravity isn't what we use anymore. In the early part of the last century, Einstein developed Special Relativity to account for the fact that light always moves at the same speed. Under SR, objects that are moving close to the speed of light see space differently than an object at rest. So just from SR considerations we know that an object whipping around a black hole at .99c is going to behave quite differently than in the Newtonian case.

Furthermore, the object is being accelerated. Einstein developed General Relativity (GR) to deal with the effect of accelerations on spacetime. In particular, gravity can be described using the solution to tensor equations. Schwarzchild was one of the first to develop a solution for these equations, and one fact that comes out of his solutions is that time runs more slowly in a gravitational field. If the mass becomes large enough, then time stops altogether: this is a black hole.

Black holes are definitely a popular subject. The page with the GR lecture notes I mentioned earlier also contains several links to other researchers description of the mathematics behind black holes.

Mark Huber