If there was no matter would space not exist also? and what if space itself is simply gravitational fields or is space nothingness?

My guess is that with no matter, there would be no space-time. But maybe there would be a kind of space that is not space-time. For time to exist, there must be matter.

My guess is that with no matter at all no one would care. Locally matter-less regions are called vacuum, and generally considered as being part of space, implying that space exists in these regions(*).

 

(*) But of course the very term "region" implies space, so the statement is circular reasoning to some extend.

@Hashirama_Senju :

You have re-discovered what Einstein called "Mach's Principle." It's actually more of Einstein than of Ernst Mach, but Mach did revive a really old gedankenexperiment called "Newton's Bucket" to argue it.

 

Interesting stuff. I've given you some search terms in the above paragraph that will lead you interesting places. If you need help with your search-fu, let me know; I will provide terms happily. You will also find a good discussion of Mach's Principle in Brian Greene's book, The Fabric of the Cosmos, which I highly recommend. I can look up the chapter if you like. It's actually a pretty direct proof of the Equivalence Principle.

Edited February 24, 201411 yr by Schneibster

There are solutions to Einstein's Field Equations with no matter or energy. Within these models, space and time exist.