Gravitomagnetism is produced by stars and planets when they spin. “It’s similar in form to the magnetic field produced by a spinning ball of charge,” explains physicist Clifford Will of Washington University (St. Louis). Replace charge with mass, and magnetism becomes gravitomagnetism.
Written out in full glory, the equations of General Relativity are intensely complicated. Indeed, they have been solved in only a few special cases. One of them is the case of weak gravity, like we experience here on Earth.
In the “weak field limit,” Einstein’s equations reduce to a form remarkably like Maxwell’s equations of electromagnetism. Terms appear that are analogous to the electric field caused by charges and the magnetic field produced by the flow of charge. The “electric terms” correspond to the gravity that keeps our feet on the ground. The “magnetic terms” are wholly unfamiliar; we don’t sense them in everyday life.
Spin (angular momentum) + “electric terms” + “magnetic terms” = Quantum gravity