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From what I remember about numerically solving differential equations, your approximations will completely diverge from the actual solution near singular points
by openasocket 10y ago
From what I remember about numerically solving differential equations, your approximations will completely diverge from the actual solution near singular points in the equation, so you have to transform the problem to come up with a singular solution. I imagine the interaction of two singularities would result in some interesting singular points. Is that what you are alluding to when you say "finding the right metrics" or am I completely off base?
In either case, could you link to one of those 2004-7 papers? It sounds like a fascinating read.
- ISL 10y agoA tricky part was making sure that numerical instabilities didn't propagate outward away from the event horizon. I believe there are now several solutions to the problem, but the one I find most intuitive is simply extending spacetime ad infinitum inside the black hole in order to allow gravitational waves to propagate inward forever. More here: https://en.wikipedia.org/wiki/Numerical_relativity https://en.wikipedia.org/wiki/Numerical_relativity