Likutei Moharan 60:5/ליקוטי מוהר"ן ס׳:ה׳

15. Fear is revealed through the effecting of special providence for barren women. Giving birth reveals fear, the aspect of “Trembling seized them there; pangs, like a woman giving birth” (Psalms 48:7). This is because giving birth causes the blood and the severities, which are the aspect of fear, to emerge. And this is especially so when a barren woman is granted special providence, since until then the blood and severities were thoroughly blocked. Therefore, afterwards, when they emerge, fear is revealed all the more.

2The extent to which fear is revealed is thus commensurate with the [number of women giving] birth. When a single barren woman is granted special providence, fear is revealed; when many women are granted special providence, there is an even greater revelation of fear. This is the aspect of “pangs, like a woman giving birth”—the extent to which fear is revealed is commensurate with the birth.

3Therefore, the granting of special providence [that led to the birth] of Yitzchak—he being an extremely potent revelation of fear, the aspect of “the Dread of Yitzchak” (Genesis 31:42)—occurred on Rosh HaShanah (Rosh HaShanah 11a). For when Sarah was granted special providence, numerous barren women were granted special providence with her, as taught by our Sages, of blessed memory.

4This is likewise the aspect of “Yet I have borne him a son in his old age” (Genesis 21:7). The birth of Yitzchak, who is the revelation of fear, brings to length-of-days/an elder, in the aspect of “The fear of God prolongs one’s days,” as explained above.