But how can the Gravitational fields curve the space, if the space doesn't contain any matter?
First of all, you must understand what is meant by curved space-time. Space-time is simply a mathematical formalism that combines space with time. In GR, space-time contains 3 spatial dimensions and 1 temporal dimension. Basically, up or down, left or right, forward and backwards along with when.
Curved space-time doesn't mean that these 4 dimensions are curved into a 5th like a rubber sheet is curved into a 3rd. The word curved is used analogously. LetÃ¢â‚¬â„¢s say we had a little detector that could detect changes in the gravitational force. Also, we are outside of a binary pulsar system. Our detector would measure that the gravitational force is fluctuating from strong to weak periodically even though we are not moving and the binary star systems center of mass is not moving. This is interpreted as ripples in space-time Ã¢â‚¬â€œ sort of like ripples in a pond. The periodically fluctuating variables that cause this gravitational force perturbation is what is meant by curved space-time. In the case I just described, the periodicity of the fluctuating gravitational field is called gravitational waves. However, if our mass isnÃ¢â‚¬â„¢t moving it would cause nearby positional and temporal coordinates to differ from those in the presence of zero mass.
As light travels in the vicinity of space-time that is curved its positional and temporal measurements would appear different to an outside observer than if the light was moving in areas of space-time that are empty. However, to an observer inside the same Ã¢â‚¬Å“curvedÃ¢â‚¬Â space it would appear that light is moving as if it were in empty space because his positional and temporal coordinates would also be different than our observer in empty space.
Why is it like this? I have no idea. But physicists have speculated that it is due to weird properties of a force exchange particle known as the graviton. The graviton hasnÃ¢â‚¬â„¢t been found, however all other known forces have exchange particles so physicists tend to believe that gravity has one as well. That part, however, is a work in progress.