The use of the word “fallen” plus the fact that this star is “given the key to the shaft of the bottomless pit” has led commentators to assume that this star is actually Satan. There are, however, no exegetical grounds for this. The essential thing to bear in mind is that the star of Revelation 9:1 falls completely under the authority and the control of the exalted Christ.
1 And the fifth angel blew his trumpet, and I saw a star fallen from heaven to earth, and he was given the key to the shaft of the bottomless pit.