The Mishna in Sanhedrin 1:5 states:
אין מוסיפין על העיר ועל העזרות, אלא על פי בית דין של שבעים ואחד.
They may not add [annex] to the city [Jerusalem] or [Temple] Courtyards, except by a court of seventy-one.
Correct me if i'm wrong, but we've been lacking a Great Sanhedrin of 71 for a while now.
The modern city of Jerusalem is much larger than the ancient city. However, even the "New City" is considered Yerushalayim. They follow the nusach of Yerushalayim, observe Shushan Purim, etc.
If the Sanhedrin never "annexed" it, how can it be part of the city?