God's throne in heaven. David's throne on earth.
God is the rightful King of Israel, and was King of Israel accepted by the children of Israel until they demanded a human king like the nations. God ruled Israel with the prophets as His spokesman. But when the Ammonites came against them, they thought they needed a human king instead of Samuel the prophet, to match up.
1Samuel 12:12 And when ye saw that Nahash the king of the children of Ammon came against you, ye said unto me, Nay; but a king shall reign over us:
when the LORD your God was your king.
When God gave them Saul as their king - He stated through Samuel that they (Israel) rejected Him (as their King).
So David's throne is, in that context, here on earth. The term messiah means anointed, and in the special case of "the" messiah, he is considered to be a descendant of David who will sit on David's throne as King of Israel the united, single nation of the twelve tribes. To lead them and the world into the messianic age of peace and safety.
There have only been three kings in that position in Israel's history. Saul, David, Solomon.
Each of those three were anointed by a prophet. Saul, David, by Samuel. Solomon by Nathan.
This gives some insight regarding the false prophet's activities beyond what it says about him in Revelation - which is post Antichrist role when it gets to Revelation 13. Before then, it is almost certain that the false prophet will be the one who anoints the little horn person, following Gog/Magog - as the King of Israel, making the person the Antichrist, for about the first three years, three months of the 7 years.
That "the Christ" son of David was equated to being the King of Israel is in...
Mark 15:31 Likewise also the chief priests mocking said among themselves with the scribes, He saved others; himself he cannot save.
32 Let
Christ the King of Israel descend now from the cross, that we may see and believe. And they that were crucified with him reviled him.
John 12:12 On the next day much people that were come to the feast, when they heard that Jesus was coming to Jerusalem,
13 Took branches of palm trees, and went forth to meet him, and cried, Hosanna:
Blessed is the King of Israel that cometh in the name of the Lord.
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The concept of the Antichrist is that he comes in his own name - someone that God did not send to be their King. And from what is written in Daniel 8 of the little horn magnifying himself in his heart, and Daniel 7 of the bragging mouth, and Daniel 11 about the king thinking he is greater than every god, and in Ezekiel 28:1-10 about him magnifying himself in his heart - the person will have the ego to think of himself as the being the messiah, and later to believe himself that he has achieved God hood.