The entry metaphysics from SEP (Stanford Encyclopedia of Philosophy) also deals with space and time, see chapter 3.2.
I am not convinced that metaphysics does contribute with any new insight to the subject. More, I suspect that the author of the entry, probably an expert in metaphysics, is not familiar with modern physics. He starts the article:
Long before the theory of relativity represented space and time as aspects of or abstractions from a single entity, spacetime, philosophers saw space and time as intimately related. (A glance through any dictionary of quotations suggests that the philosophical pairing of space and time reflects a natural, pre-philosophical tendency: “Had we but world enough, and time …”; “Dwellers all in time and space”.)
The examples cited above consider two separate entities, 1) space and 2) time, which are a “philosophical pairing”. But spacetime is not just adding space and time. One of the main conceptual changes of special relativity was to introduce 4-dimensional spacetime as its basic concept. There is a certain freedom how to decompose spacetime into a component space and a component time. The decomposition depends how the observer chooses its frame of reference.
The single invariant entity in spacetime is the light cone. It separates my future and past from my present. I am causally connected to all events within my light cone, but to none event outside my ligth cone. Hence the special theory of relativity operates with the basic entities spacetime and light cone. From them it derives space and time and the first causal relations.
From this point of view one can easily answer the question raised in SEP about whether space and time are real. If one takes real in the sense of “existing independently from any observer” then the answer is: No, space and time are not real, because they depend on the choice of reference. But spacetime is real, because it is an absolute, not a relative concept. One could ask at this point: Can we close the discussion now?
But the entry in SEP, which runs under the heading “The modern metaphysics”, continues to bring into dicussion the God concept. In my opinion, we should have learnt the lecture from history of science: It it always confusing when mixing scientific questions with theological or even religious ones.
I know that my question makes clear that I neither see nor expect any results from metaphysics concerning spacetime and the derived concepts of space and time. But I am also sure that my question
Should time and space be considered a subject of metaphysics?
will not fit the high estimation of metaphysics by other participants of StackExchange Philosophy. Therefore I hope to learn now the arguments of the adherents of metaphysics.