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Can a black hole collide with the Sun?

What will happen in that case? Will the Sun survive?

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Yes, in theory. But;

No, this is very unlikely to happen during the life of the sun. If it did happen it would be Bad.

Many black holes are much more massive than the sun, even though they are much smaller. If a black hole were to enter the sun, some the matter that forms the sun would form into a accretion disc around the black hole and eventually fall into the black hole. The rest of the sun would be utterly disrupted by the massive release of energy as matter falls towards the black hole.

The solar system would be wrecked. The Earth, even if it survived intact, would not be able to support life.

Fortunately black holes are rare, and space is BIG. The chances of a black hole coming anywhere near the sun in the next billion years or so is very very small. There are more pressing things to worry about.

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The Sun would drown in the endless gravity well of the black hole, if they collide head on. The black hole would radiate nothing, unless from a disc surrounding it if more matter happens to fall into it. Sun grazing comets would make it flash a bit now and then. The sunlight would be gone, trapped beyond the horizon of spacetime. The planets would freeze air to ice as they continue in their orbits, disturbed and quite a bit faster since the new Sun+BH center is much more massive, without any sunlight hitting them. But perfect constant night sky conditions for amateur astronomers btw :-)

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