Does the concept of Brahma muhurta (time of Brahma) exist in Buddhism? On Buddhist retreats and at most Buddhist monasteries the morning meditation session is at around 4:30 or 5:00 am.


  In Hinduism, Brahma muhurta (time of Brahma) is a period (muhurta) one and a half hours before sunrise or more precisely 1Hr 36 Mins before sunrise. i.e. 96 Minutes = 2 Muhūrta or 4 Ghaṭīkā,and each Muhurta lasting for 48 minutes. Literally meaning "God's Hour", it is traditionally the last phase or muhurta of the night and is considered an auspicious time for all practices of yoga and most appropriate for meditation, worship or any other religious practice.    


Source: https://en.wikipedia.org/wiki/Brahmamuhurtha

Is there a similar theoretical basis in Buddhism? If so, where can I learn more about it?

Side note: I've been automatically waking up at 4:00-4:30 am now for sometime now without intending to. It doesn't matter how tired I am, or how late I go to bed, I come fully awake at this time, and my eyes aren't burning or showing any signs of fatigue. I'll sit up and mediate in bed after a little washing up. After an hour or so (actually 48 minutes sounds about right, I don't set a timer so I can't confirm) I will go back to bed or about the day after a little more meditation, depending on my schedule. I find this automatic process quite fascinating. That's how I started to research this phenomenon.
I am unable to find a reference, but I have heard at a Dhamma sermon that the Buddhist monks are advised to get up at 4 in the morning, then clean the mouth and have a light soup which consists of salt, water and may be some other ingredients.(A light soup with salt in it) After that monks are advised to learn the Dhamma, may be memorizing, understanding etc. So yes it is advised to get up at 4 am and study but I am not sure whether the term Brahma Muhurtha is used in that scenario. Outside the Dhamma, many studies have been done on morning people and they have been found to be more successful, proactive and happier. 

http://www.inc.com/news/articles/2010/07/research-says-morning-people-are-more-proactive.html
http://www.prevention.com/health/sleep-energy/study-finds-morning-people-are-happier

Laymen also can follow these steps and can become happier and more successful in reaching their visions.