Answer

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The bottle has been heated in boiling water. That´s why the air in the bottle is hot. The egg is put on the bottleneck in a way that it entirely closes it up. The air pressure in and outside the bottle is exactly the same (see below. Within minutes the air inside the bottle cools down causing a lowering of air pressure inside it (see smaller arrow below).

Since external air pressure is bigger than internal air pressure the egg is beeing forced into the bottle (see picture below).