Physicist: The side of the Earth facing the sun would quickly become hotter than boiling water, and the side facing away would be cold enough for the atmosphere to freeze solid (condense into nitrogen and oxygen ice). So all of the air and water would form glaciers of ice and what-was-once-air on the night side of the planet, and the day side of the planet would become an airless desert. Without air to scatter sunlight, the sky would always be black, and the stars always visible.

Here I’m assuming that the Earth, rather than not rotating at all (which would result in one-year-long days), is in “phase lock” with the Sun the same way the Moon is in phase lock with the Earth. So one side would always face the Sun and the other would always face away.

We can estimate how hot and cold things would get by considering the Moon. It’s the same distance from the Sun as the Earth is, so it’s a good test case. Very quickly (within a few minutes) after the Sun rises at the beginning of the Moon’s 709 hour day the surface gets about as hot as it’s going to get: a balmy 110°C/230°F (give or take).

Some craters on the moon are never exposed to sunlight at all, which is exactly the situation the dark side of the Earth would be in, writ small. They get as cold as -240°C/-400°F (that 30°C above absolute zero!). That’s cold enough to freeze oxygen and nitrogen solid, even without air pressure. So on the day side everything would get roasted, the oceans would evaporate out of their basins, and then drift to the dark side where they would form and condense onto massive glaciers.

For water at least, this is an effect already at work on our Earth (“spin Earth”?, “Rotopolis”?), it just doesn’t get very far. That’s why (for example) the Antarctic ice cap is on average about as thick as the ocean is deep!

The non-rotating planet is a staple of sci-fi, and generally it’s declared that life could survive in the “twilight ring” between the day and night sides. In fact, in the twilight ring the temperature would be colder than our poles are today (which are kinda like “twilight points”). You find the “comfortable zone” about 20° into the day side from the ring.

Not that it matters. What with the atmosphere being in such a state that you’d need a hammer and chisel to breathe, it wouldn’t be possible for life to exist anywhere. The set up we have now is pretty good by comparison!