How long would the Earth last if the sun became a black hole?

[halfeye]

From our point of view, time dilation included, how long would we last if the Sun became a black hole?

We'd all be dead from the supernova that comes first, wouldn't we? Is there any way that wouldn't happen?

The sun is not going to go supernova, at all, so long as it doesn't ingest twice its current weight in hydrogen (or other mass, but hydrogen is the most common free gas, and ingesting a bigger star would be the bigger star eating the sun).

If the sun was suddenly replaced with a black hole, we'd freeze, very quickly. The air would be frozen out in hours, and the temperature at the surface would drop cllose to the temperature or the cosmic background radiation (2.3 Kelvin?) in days. The core would probably freeze eventually, but since most of that's nuclear, maybe not.

There would be less than a week to organise a heated space, and I'd bet humanity couldn't stop arguing long enough to do it. We would need a population of over a hundred to survive.