In Greg's Emptiness group in Facebook, Elaine Catton posted:
Taking the following quote from the Dalai Lama, regarding the Clear Light, how is Clear Light understood in the emptiness teachings?

""Dodurupchen says that all phenomena are quite definitely such that they arise as rigpa energy or rigpa display. From the point of view of the new schools of tantra (sarma), everything that appears arises as the display of great bliss, and the display of emptiness. In the terminology of Dzogchen whatever manifests arises as the display of rigpa, and that is certain. So the agent responsible for all of this as well as the space and ground for it all, is the single state of Clear Light. Everything, in fact , is the display or array of Clear Light. Such experiences of Clear Light will arise, and when they do, you are left without any fear of falling into samsara: you are left without any hope of attaining nirvana: you are left without any hope or fear whatsoever. All experiences and all feelings, be they good or bad, karma, its results, birth and death and change: all of this manifests as the magical display of Clear Light."

Dzogchen by the Dalai Lama pp 196 and 197

I replied with my limited knowledge on this subject:

Posted this before:

The Dalai Lama has this to say:

http://awakeningtoreality.blogspot.sg/2009/07/happiness-karma-and-mind.html

"...We have become so habituated to consciousness of the form and color of gross objects that, when we make concentrated introspection into the nature of mind, it is, as I have said, found to be a vast, limitless void free from any gross obscurity or other hindrances. Nevertheless, this does not mean that we have discerned the subtle, true nature of the mind. What has been explained above concerns the state of mind in relation to the concrete experience and clear cognizance by the mind which are its function, but it describes only the relative nature of mind."

"...However, as we have observed, its true nature has many aspects, including consciousness of concrete experience and cognizance of objects. Now let us make a further examination in order to grasp the meaning of the subtle essence of such a mind. Mind came into existence because of its own cause. To deny that the origination of mind is dependent on a cause, or to say that it is a designation given as a means of recognizing the nature of mind aggregates, is not correct. With our superficial observance, mind, which has concrete experience and clear cognizance as its nature, appears to be a powerful, independent, subjective, completely ruling entity. However, deeper analysis will reveal that this mind, possessing as it does the function of experience and cognizance, is not a self-created entity but Is dependent on other factors for its existence. Hence it depends on something other than itself. This non-independent quality of the mind substance is its true nature which in turn is the ultimate reality of the self. "

It may be further questioned on the Dalai Lama's position: this subtle, relative nature of mind, which is not merely gross sensory objects and thoughts but which even seem like a void and illuminating source, how can that be said to be non-independent? It seems to be non-arising and non-dependent.

What the Dalai Lama calls the 'subtle clear light' is indeed non-arising like anything and everything due to its empty nature, but in emptiness teachings we do not treat it as having some special or ultimate status of being a 'powerful, independent, subjective, completely ruling entity'.

It is never lost but is seen as a stream... as the Dalai Lama considers that this clear light mind is "permanent not in the sense of not disintegrating moment by moment but in the sense that its continuum is no interrupted…" (http://www.dreamyoga.com/tibetan-dream-yoga/the-dalai-lama-on-the-clear-light) In other words this mind of Clear Light, which is pure Knowingness and luminosity as described there, is not unchanging as a static substratum but as an uninterrupted flow like a mighty river. Luminosity will never be lost, so it is like a vajra (diamond), but not in the sense of a substantiated entity. It is not a background source behind manifestation but we see that the source is in fact manifestation itself - it is the flow of knowing without knower, in all manifestation and differentiation we experience the same taste of luminosity and emptiness.

Elsewhere such as http://newbuddhist.com/discussion/14234/fundamental-innate-mind-of-clear-light - the Dalai Lama furthermore clarifies the non-independent, causal nature of clear light.

Geoff (jnana/nana) from Dharmawheel sums up this view:

"...For example, Sajjana's Mahāyānottaratantraśāstropadeśa equates tathāgatagarbha with luminous mind, and then explains that although this luminous nature is not-conditioned (unlike ordinary states of mind that are contingent upon the four conditions), the luminous nature arises due to the previous moment of that same luminous mind. Shakya Chogden has a similar understanding, stating that although the tathāgatagarbha is often said to be permanent, etc., "that is also done in terms of its continuum. Otherwise, [it should] be [understood as] impermanent, precisely because of having an immediately preceding condition [deriving] from [its previous] moment."

"...Again, Tibetan commentators such as Go Lotsawa maintain that space is also momentary. Relying on the Dharmadharmatāvibhāgavṛtti, he states:

It is not the case that space that exists only as enclosed space does not partake of the nature of momentariness along a continuum. If you take time into account here, space at the beginning of an eon (kalpa) is not the [same] space at the time of [its] destruction. In terms of location, the substance that exists as the enclosed space of a golden receptacle is not that which exists as the enclosed space of an earthen receptacle.

He then applies this analysis of space to the buddha element:

Likewise, a moment in the continuation of a continuum having the quality of the [buddha] element's awareness of sentient beings is not a moment in the wisdom of a buddha. Notwithstanding, in the same way as the existence of the enclosed space of a golden and earthen receptacle is not different in terms of type (rigs), the nonconceptuality of a buddha and the nonconceptuality of sentient beings are of a very similar type." .

In the above quotations, Dalai Lama made it clear that the "concrete cognizance" of mind (clear light/luminosity) is still the relative/conventional nature of mind, while the ultimate nature of mind is its emptiness. Awareness itself is conventional and empty! 'Awareness' is like the word 'chariot' or 'self', not a singular, independent and irreducible ("It's all just One Awareness") kind of substance or reality that can be pinned down somewhere apart from the various streams of dependently arisen consciousness (or revealing its actual state as the five wisdoms, when in knowledge) empty of any core or self/Self.

Similar statements can be found elsewhere such as http://www.byomakusuma.org/Teachings/InterviewWithKhenchenRigdzinDorjeOnTheNyingmapaView.aspx

"Khenpo: According to the Nyingmpa, the luminosity can be experienced as pure or impure but the ultimate truth is emptiness. We have two types of conventional truth, one is pure and one is impure. The conventional truth of the ordinary man is impure, while the conventional truth of the Buddhas is permanently pure.

Ratnashree: So, salwa/luminosity/prabhashwar is still conventional. It is pure or impure but still conventional?

Khenpo: Yes

Ratnashree: Only emptiness is the ultimate truth?

Khenpo: Yes

Ratnashree: We have 1) self emptiness view, that is Rangtong/Swa Sunya view/Tawa/ Dristi and 2) other emptiness view Shentong/Para Sunya view/Tawa/ Drishti, etc. What is the official Nyingmpa view (Tawa/Dristi)? What is the view of Longchenpa, Mipham, Jigme Lingpa etc.?

Khenpo: According to the Nyingmapa, we are not Rangtong, we are not Shentong. If you believe only Rangtong, it becomes nihilistic (ucchedvad). If you believe only Shentong, it becomes eternalist (saswatvad). We believe in Sung Zhug/Yuganadh or Abheda (the indivisibility of or unity of clarity and emptiness/ Prabhaswar Sunyata Yuganadha). According to the second turning of the wheel, all the appearance itself is emptiness .That is Rangtong/Swasunyavadin. According to the third turning of the wheel, we can say that there is some pure vision which the Buddha can see. That is called Shentong/Parasunyavadin. But these two are united. Pure vision and emptiness are united primordially. And that is the Sung Zhug view, Abhedavadin or Yuganaddhavadin, ‘Indivisible-ist’ so to say. Therefore, we are not Shentong and not Rangtong.

(NB: Actually when it comes to actual meditation the Sakya meditation view is also what the Khenpo here calls Sung Zhug. Rangtong in the Sakya system actually means that the emptiness of the Prasangika is not abandoned in the ultimate truth and in Sung Zhug this emptiness (niswabhavata) or empty of real self existence is not abandoned. And regarding luminosity/clarity (prabhashwar) being the conventional truth, regardless of whether it is pure or impure, it is also the view of the Mahasiddha Virupa, which makes it the official Sakya view;( prabhaswar/luminosity/clarity/awareness by itself is the conventional truth)

........

(end of excerpt)

But with regards to the original teachings of Nagarjuna or Madhyamika studies in general, I think not much is spoken about clear light/luminosity, unless you consider treatises (which is attributed to but not likely to be actually written by, Nagarjuna) like In Praise of the Dharmadhatu to be the actual writings of Nagarjuna, which I think is great regardless of who wrote it.

Clear Light however is spoken in all four traditions of Tibetan Buddhism and if you are talking about Tibetan Buddhism as a whole and not just Madhyamika teachings, then you will find abundant teachings about the inseparability of luminosity and emptiness.