Re: [math-fun] dumb question re GR -- 2-body simulators on the web?
I'd like to redo Newton's "cannon on a mountain top" thought experiment again, except using GR instead of Newtonian gravity. If you recall, the cannon is on a mountain top on the Earth & it fires a cannonball at various velocities parallel to the Earth's surface. With enough velocity, the cannonball "falls", but not fast enough to actually hit the Earth's surface, and therefore comes all the way around the Earth & its path becomes an orbit. I'd be interested in finding a GR 2-body simulator that handles 1 black hole plus a particle of very small mass, or 2 black holes of various masses -- i.e., it should be capable of handling extremely large gravitational forces. Since there are only 2 bodies, we need only 2 space dimensions plus time. With only 2 bodies, we could also utilize the 3rd dimension to show distortion of spacetime. We can center the picture at the center of mass. I don't know whether it's possible or reasonable to utilize a frame of reference that rotates with angular momentum. We should be able to scale the various space & time dimensions to watch interesting behaviors. I did a Google search, but was unable to find such a simulator. Does anyone know if such a GR 2-body simulator exists on the web?
From: Henry Baker <hbaker1@pipeline.com> To: Mike Stay <metaweta@gmail.com> Cc: math-fun <math-fun@mailman.xmission.com>; mcintosh@servidor.unam.mx Sent: Sunday, July 26, 2009 12:23:58 PM Subject: Re: [math-fun] dumb question re GR -- 2-body simulators on the web? I'd like to redo Newton's "cannon on a mountain top" thought experiment again, except using GR instead of Newtonian gravity. If you recall, the cannon is on a mountain top on the Earth & it fires a cannonball at various velocities parallel to the Earth's surface. With enough velocity, the cannonball "falls", but not fast enough to actually hit the Earth's surface, and therefore comes all the way around the Earth & its path becomes an orbit. I'd be interested in finding a GR 2-body simulator that handles 1 black hole plus a particle of very small mass, or 2 black holes of various masses -- i.e., it should be capable of handling extremely large gravitational forces. Since there are only 2 bodies, we need only 2 space dimensions plus time. With only 2 bodies, we could also utilize the 3rd dimension to show distortion of spacetime. We can center the picture at the center of mass. I don't know whether it's possible or reasonable to utilize a frame of reference that rotates with angular momentum. We should be able to scale the various space & time dimensions to watch interesting behaviors. I did a Google search, but was unable to find such a simulator. Does anyone know if such a GR 2-body simulator exists on the web? _______________________________________________ The first problem, a test particle in orbit about a black hole, is just the equation of a geodesic. It is solved in almost any textbook on general relativity. The second problem, that of two black holes, is nontrivial, and is a topic of current research. There does not exist a static solution since there will be gravitational radiation, leading to the eventual merger of the black holes. Google search for "black hole merger". The first hit is a movie that may possibly be helpful. -- Gene
Sounds like the evolution of the banking system. :-) I watched the movie you referenced, but the downloadable version was at too low a resolution & went by too fast to get any better understanding of what was going on. I assume that you mean that _any_ configuration of exactly 2 black holes -- regardless of size ratio, energy & angular momentum -- will eventually merge into one black hole, with the emission of gravitational radiation. Even dumber question: what eventually happens to the resulting black hole & its gravitational radiation? In the classical GR case, is this an infinite universe? At 02:17 PM 7/26/2009, Eugene Salamin wrote:
The second problem, that of two black holes, is nontrivial, and is a topic of current research. There does not exist a static solution since there will be gravitational radiation, leading to the eventual merger of the black holes. Google search for "black hole merger". The first hit is a movie that may possibly be helpful.
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Eugene Salamin -
Henry Baker