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

[Radar]

OK, let's use that desert example. In the first 12 hours without sunlight, temperatures drop by over 40º. If that rate holds up, it'd take three days to get down to -200º, for the nitrogen to condense out of the air. And that rate won't hold up, because heat loss by radiation is strongly dependent on temperature, so as the temperature drops, the rate of temperature decrease will slow dramatically. And now consider that, over timescales of multiple days, heat transfer from elsewhere on Earth will be relevant, and most of the Earth's surface is covered with water.

The thing is, conditions will stop being livable way before we hit -200º. -20º in areas that are ill prepared for below 0º temperatures will be deadly enough. At any rate, the timescales allowing short-term survival will not be long enough to prepare lasting solutions as the economy network could not be maintained. Even with the currently available technology and infrastructure preparing habitats in mineshafts would take quite likely months. Weeks maybe if we disregard safety procedures and any kind of planning.