In Bhagavatī-sūtra (Vyākhyā‑prajñapti), these are technical terms used when describing the beings in Narak (hells), devas, etc.:

1. Upapāt‑viraha‑kāl (upapat viraha kaal)

- Upapāt / Upapātī = spontaneous birth (without parents, like hell‑beings, many devas, etc.). - Viraha‑kāl = the “interval of absence”, a gap in time when that event does not occur. - So upapāt‑viraha‑kāl means: > The period of time during which, in a particular group or place (e.g. a specific Narak), no new beings take birth by upapāt (spontaneous birth). - It is used when discussing whether births in a certain hell, or class of beings, occur continuously (niraṅtara) or with gaps (saṅtara). The “gap” side is expressed by this viraha‑kāl.

1. Udvartana‑viraha‑kāl (udvartan viraha kaal)

- Udvartana (in this context) = the “coming out” or leaving of a being from that state – i.e. completing that ayuṣya and exiting that Narak / loka. - Udvartana‑viraha‑kāl therefore means: > The period of time during which no being leaves (no udvartana occurs) from that particular Narak or class of beings. - Again, this is used to discuss whether departures from a certain hell occur one after another without any break, or whether there can be intervals of complete absence of such departures.

So, very simply:

• Upapāt viraha kāl = minimum/possible gap when no new births happen in that realm.
• Udvartana viraha kāl = minimum/possible gap when no exits/deaths happen from that realm.

These notions help Bhagavatī‑sūtra systematically analyse whether the rise (utpatti/upapāt) and fall (udvartana) of jīvas in naraks and other gatis are continuous or have intervals.