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Concentrating a lot of matter in one place will make a black hole, not a wormhole. A wormhole would change the topology of spacetime. Does General Relativity allow this?

I know there are wormhole solutions to GR field equations, but they are static solutions. Is there a time evolving solution to the GR equations in which a flat region of spacetime transforms into a wormhole geometry/topology due to an appropriate inflow of matter and energy and negative energy?

What determines where the other mouth of the wormhole forms?

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