Is it a good idea to continue a PhD with an advisor who doesn't really know your field? Some background:


I started my PhD in Machine Learning in April this year.
My PhD is fully funded for 3 years, I earn around 2000€/month after tax, working only on research and not doing any teaching.
I'm paid by the grant that my advisor got for his project. This grant his paid by the state.
My current advisor is a world expert in Machine Learning
I already submitted 2 papers with him and most likely submit a third one in a couple of months.


The problem: My advisor just got an offer from one of the biggest company you can think of, to do a machine learning project with lots of different world experts newly hired by the said company. It means that he is going to leave his current position at my university in 4 months. 

I can't blame him to take this position because I would have done the same. It's an offer that nobody can refuse.

So in 4 months, I'll have to make a choice.


leave my position and look for a position elsewhere but I doubt I'll find something as interesting and well paid. (My advisor can write recommendation letter for me.)
to stay at the university and choose a new advisor -> the problem is that my current research is highly technical and nobody except my current advisor (and I) have knowledge about it (he was a new junior professor and the university wanted to expand the CS department). The rest of my group is working on a totally different subject and I know nobody will be able to help me for the rest of my PhD.


My advisor told me that the university will find me a new advisor if I choose to stay but warned me that my topic will most likely shift to adapt to the domain knowledge of this new advisor. It means that I'll have to give up my current topic and to tell you the truth, I prefer to quit my PhD than to continue on something that I don't like.

For info, I read this post how-to-cope-when-phd-advisor-quits-midway but I think my problem is slightly different.

tldr: Is it possible to do a PhD with an advisor that can't help you? Or is it better to just go somewhere else?
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!