Is lucifer chained up in hell?

In various religious and mythological narratives, Lucifer is often depicted as a fallen angel who rebels against God. In some interpretations, especially within Christian theology, he is believed to be cast out of heaven but not necessarily chained in hell. Instead, he is often portrayed as roaming the Earth, tempting humans. However, certain apocryphal texts and interpretations suggest that he may be bound at times, particularly during apocalyptic events.