There is no climbing rope in the hole at the bottom of the sinkhole. Actually the little hole is under water so you will have to dive to go down there. To enter the sinkhole you have to go through some caves and i believe the cave entrance is in the east of the sinkhole, a few meteres away, next to the river. To open the metal gate which blocks your way into the sinkhole you have to place some heavy items on a nearby "plate". About 3 stones might be enough. When you dive down the little hole in the middle of the sinkhole it says "FOLLOWING AREA NOT YET AVAILABLE" or something like that. I hope i helped.