Wearing a Wristwatch Without an Eruv

Is it permissible to wear a wristwatch in a place where there is no eruv?

Greetings,
A watch that serves as jewelry, regardless of its time-telling function, is permissible to wear in a place where there is no eruv.
A watch that primarily serves to tell the time, even if it is beautiful, is forbidden in a place without an eruv.
Generally, the distinction is between women's watches, which are primarily for adornment, and men's watches, which are primarily for telling time. However, each person and each watch should be considered individually. One should ask oneself whether one would wear it even if it did not show the time.

Shulchan Aruch, Orach Chayim, 308