Gödel and Einstein

For quite a few years, Gödel and Einstein were both at the Princeton Institute for Advanced Study. Quoting from Albert Einstein: Historical and Cultural Aspects (Gerald Holton and Yehuda Elkana, editors):
The one man who was, during the last years, certainly by far Einstein's best friend, and in some ways strangely resembled him most, was Kurt Gödel, the great logician. They were very different in almost every personal way - Einstein gregarious, happy, full of laughter and common sense, and Gödel extremely solemn, very serious, quite solitary, and distrustful of common sense as a means of arriving at the truth. But they shared a fundamental quality: both went directly and wholeheartedly to the questions at the very center of things.
Gödel did original work in relativity theory by finding a new class of solutions for the field equations of general relativity, the so-called "rotating universes" or "Gödel universes".