Is it a good idea to continue a PhD with an advisor who doesn't really know your field?
judging nobody knows the area except you and your advisor seems
a strong statement to me specially if you just started doing research
(this April ). 

I am quite sure there are other folks working on the same topic or
something really close to it. Those are your potential advisors. 

Taking into account that you just started and he's a world class
expert, I believe the best thing is to approach your advisor asking
for help. Ask him to suggest some names to you.  He certainly
knows other academics and can even approach them asking for a PhD
position for you (have you looked to his co-authors list in DBLP for
example? ). I have heard several cases where advisors help their
students secure PhD positions in other institutions.
Take a breadth view over other's research. Attend their seminars. You
might see their work interesting as well.
DO NOT LOSE YOUR ADVISOR. keep in touch with him and try to be his student even outside academia!