In most grammar books, adjective/relative clauses are limited to specific constructs involving words such as 'that' or 'which' (as two of multiple examples):
[1] The house that I grew up in
There are also examples of non-finite relative clauses, which use participles and infinitives:
[2] The man speaking on the stage
[3] The best time to be alive
However, there are other examples that are rarely spoken about. Consider these:
[4] The time before he found his calling
[5] The moment after she discovered the truth
[6] Life as we know it
In the grammar resources that I have read, these types of clauses are always presented as adverbial, usually modifying a verb. Clearly, this is not their sole function. That being the case, are the examples above (4–6) correct? They are often used in both informal and formal English, so why do most resources neglect to mention them? If they are correct, would we class them as relative clauses?