Is it permissible to apply a pain-relieving ointment to the gums while fasting, or to undergo a surgical procedure to extract a wisdom tooth and remain fasting under the influence of anesthesia?

It is permissible to treat teeth and apply ointment or similar substances to the gums for a fasting person, provided that nothing from it is swallowed. The book "Seventy Issues in Fasting" by Sheikh Muhammad Salih Al-Munajjid mentions that among the things that do not break the fast are: medicinal tablets placed under the tongue for angina pectoris if one avoids swallowing anything that reaches the throat, drilling a tooth or extracting a molar or cleaning teeth and using a miswak and toothbrush if one avoids swallowing anything that reaches the throat, and rinsing the mouth (madmadah), gargling (ghurgharah), and topical mouth spray if one avoids swallowing anything that reaches the throat. Furthermore, there is no harm in undergoing a surgical operation during the daytime in Ramadan under the influence of anesthesia, as long as the anesthesia does not last the entire day, for the ruling on anesthesia in that case is the same as that of sleep.