Here is a summary from Tsele Natsok's Heart Lamp (p. 31-33) on the nine dhyanas. Interestingly, it is not under the section discussing shamatha but the chapter about "Faults and Qualities", sub-chapter "Clearing Away Specific Errors and Mistakes". The reason given is the fault of attaching to bliss, clarity and nonthought. What he originally defines as the proper practice of shamatha in Mahamudra is resting naturally without fixating on thoughts or appearances. So, his description of the dhyanas:
When resting evenly in shamatha, then, to be free from gross thoughts of perceiver and perceived, but still to be fettered by the concept of meditator and meditation object is called the "samadhi of the First Dhyana." Why is that? Because this is what is being meditated upon in all the abodes of the gods of the First Dhyana. Meditating in this way creates the cause for being reborn there as a god at the level of the First Dhyana.
Likewise, the second dhyana is to be free from the state of mind of concept and discernment, but still to experience the taste of the samadhi of joy and bliss.
The third dhyana is to be free from mental movement, but supported merely by the inhalation and exhalation of breath.
The fourth dhyana is to be free from all kinds of thoughts, a state of samadhi which is unobstructed clarity, like space.
Supreme among all the mundane samadhis, these are the foundation for vipashyana. If meditated upon with attachment, however, they become a deviation from Mahamudra causing rebirth as gods in the abodes of those dhyanas.
Furthermore, thinking "All phenomena are infinite like space!" or "This consciousness, free from partiality and nonexistent, is infinite!" or "Perception, being neither existent nor nonexistent, is not an action of mind!" or "This mind is voidness, which is nothing whatsoever!"Dwelling in the states of these four levels has the defect of straying into the four formless spheres of finality; called the Infinite Space, Infinite Consciousness, Neither Presence nor Absence, and Nothing Whatsoever.
The shravaka's samadhi of peace is the state of mind that has abandoned these four thoughts in which involvement in objects has been blocked, and in which you abide having interrupted the movements of the wind-mind. Although such a state is taught to be the ultimate shamatha, in this context it is not a faultless meditation unless embraced by vipashyana.
Each of these nine dhyanas of absorption has some temporary qualities, such as accomplishment of superknowledges and miraculous powers. Here, however, you should attain the ultimate result of complete enlightenment and not merely relative or superficial qualities. Thus, if these are accomplished naturally and you then cling to them or feel arrogant, know that to be a direct obstacle for enlightenment.