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Wormhole is yet to be discovered but it is predicted by general relativity, when mass is added into a black hole its event horizon grows bigger. I want to know how the mathematics of general relativity suggests a wormhole is actually a black hole with a throat.

What happens to the mass and can massless wormhole exist in nature?

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You say:

I want to know how the mathematics of general relativity suggests a wormhole is actually a black hole with a throat?

but I suspect you are mixing up two different things. The geometry of a maximally extended Schwartzschild black hole contains a structure that looks a bit like a wormhole, but this is not a wormhole that anything can pass though. Furthermore the maximally extended Schwarzschild black hole is a mathematically idealised black hole that cannot exist in the real universe so we can be confident that Schwarzschild wormholes don't exist.

The structures so beloved of science fiction writers are more like the Morris-Thorne wormhole. This is not associated with a black hole and is kept open by using exotic matter (which as far as we know does not exist). The mass of a Morris-Thorne wormhole is predominantly the mass of the exotic matter that is being used to stabilise it, so its mass will depend on how exactly it has been constructed.

Finally you ask if a massless wormhole can exist. No wormhole, or at least no traversable wormhole, can exist without associated exotic matter to stabilise it so in this sense the answer to your question is no. Associating a mass with the wormhole utself is a somewhat tricky task. Presumably this would be the ADM mass, but I'm not sure what the physical significance of this is for a wormhole.

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