That time around 4 am is known as "the hour of the wolf" in swedish. It's the time of the night when the body's activity is at its lowest. The melatonin levels are at its highest, body temperature and blood pressure reach their lowest levels and metabolism goes down.
The conditions for being awake is at its worst at this particular time. All of these factors means that you usually sleep through these hours, but if you wake up, the body is extra vulnerable, and you usually don't feel so good. Your psychological defenses are down, and the things you hide and fear might become very apparent.
“The Hour of the Wolf is the hour between night and dawn. It is the hour when most people die. It is the hour when the sleepless are haunted by their deepest angst, when ghosts and demons are most powerful." - from The Hour of the Wolf by Ingmar Bergman