Motivated by this question: Perturbation of a Schwarzschild Black Hole
How would one deal with the situation where black hole experiences not only small perturbations but major changes to the metric?
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Like in most physically complicated cases, one would normally solve the dynamic system numerically. In the case of general relativity, the "3+1 decomposition" method or equivalent is used. There are some open source tools for aiding in numerical research.
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