Suppose the sun were to suddenly become a black hole
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Answer:
Earth would then be a black hole! If the Sun were somehow compressed enough to become a black hole, it would be less than 6 kilometers (well under 4 miles) across. It would exert no more gravitational force on Earth or the other planets in the solar system than it does now.
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Answer:A lot would go wrong. Its not about getting sucked in. The Schwarzschild radius of such black hole would be about 3 km. It won't suck anything in unless it is too close. Like Sun, black holes too have a finite amount of life time. They evaporate. This evaporation time decides their life span. A black hole with the same mass as that of Sun would take incredibly long amount amount of time to completely evaporate. If you calculate, it turns out to be 2 x 10^67 years, whereas our Sun has 4 billion years to go.
The current age of the universe is only 13.8 billion years. It means that it will take more than 10^57 times the current age of the universe for such a black hole to evaporate.
At the exact moment the Sun would be replaced by a black hole, we would have no idea because the light from the sun takes 8.3 minutes to reach the Earth.
With no sunlight and the moonlight the universe itself would be out only source of visible light from space. There would be enough light from space for us to see around a bit. Electricity and fossil fuels would be usable for a while so cities and towns could continued to be lit by man-made sources just like a typical night. Except, it would be night everywhere. Photosynthesis would stop immediately. 99.9% of the natural productivity on earth is done by photosynthesis, which requires the Sun. Our plants and trees would die out in a time span ranging from a few days to few years.
Another problem is going to be that the Earth will get quite cold. Right now, with our Sun, the average surface temperature on Earth is an arguably comfortable 14-15 degrees Celsius. Without the Sun to add energy, the Earth would radiate away heat exponentially. By the end of the first year without the Sun the average global surface temperature would be -73 degrees Celsius. Nearly all life on earth exists because of and is dependent upon extraterrestrial energy- The Sun.
But the Earth produces its own heat. Despite the coldness of space for indefinite amount of time, down below the crust, the earth is quite warm. Deep in it's core radioactive elements decay, providing the energy needed to keep the earth's core at 5000 degrees Celsius.
A year or so after the Sun disappeared, the earth's oceans will have frozen over. Ice all the way across. But ice is less than liquid water which means that ice floats. And ice is a decent insulator. So for billions of years after the Sun is replaced, liquid water could still exists at the bottom of our oceans protected and insulated from space by miles of ice above it and warmed by the ocean floors from earth's interior.
Its amazing to think that life(at least in form of microorganisms) here on earth all alone flying through space with no Sun would kind of be fine because of the enough geothermal heat for billions of years.