Are big cats domesticable?

Can you domesticate big cats like lions, tigers, and cheetahs? The Egyptians worshipped cats and the sphyinx portrayed the head of a pharaoh and the body of a lion. They obviously had big cats as well as small cats. But how did they not get maimed and killed by the larger cats? And if the Egyptians did keep large cats, how come we can't now?