surrogate mother

Attention Rabbi Dr. Mordechai Halperin.

Dear Rabbi,

I recently returned from a trip to the States and was asked the following questions by Prof. Michael Rosen of Columbia University:

If an egg from a Jewish woman is implanted into a non-Jewish surrogate mother, is the resulting child/baby Jewish?

If an egg from a non-Jewish woman is implanted into a Jewish surrogate mother, is the resulting baby Jewish?

Is there a halachic ruling regarding the above two questions?

I would really appreciate an answer.

Thanking you,

Yours sincerely,