Objection 1. It would seem that judiciary power is not to be specially attributed to Christ. For judgment of others seems to belong to their lord; hence it is written (Romans 14:4): "Who art thou that judgest another man's servant?" But, it belongs to the entire Trinity to be Lord over creatures. Therefore judiciary power ought not to be attributed specially to Christ.
Objection 2. Further, it is written (Daniel 7:9): "The Ancient of days sat"; and further on (Daniel 7:10), "the judgment sat, and the books were opened." But the Ancient of days is understood to be the Father, because as Hilary says (De Trin. ii): "Eternity is in the Father." Consequently, judiciary power ought rather to be attributed to the Father than to Christ.
Objection 3. Further, it seems to belong to the same person to judge as it does to convince. But it belongs to the Holy Ghost to convince: for our Lord says (John 16:8): "And when He is come," i.e. the Holy Ghost, "He will convince the world of sin, and of justice, and of judgment." Therefore judiciary power ought to be attributed to the Holy Ghost rather than to Christ.
On the contrary, It is said of Christ (Acts 10:42): "It is He who was appointed by God, to be judge of the living end of the dead."
I answer that, Three things are required for passing judgment: first, the power of coercing subjects; hence it is written (Sirach 7:6): "Seek not to be made a judge unless thou have strength enough to extirpate iniquities." The second thing required is upright zeal, so as to pass judgment not out of hatred or malice, but from love of justice, according to Proverbs 3:12: "For whom the Lord loveth, He chasteneth: and as a father in the son He pleaseth Himself." Thirdly, wisdom is needed, upon which judgment is based, according to Sirach 10:1: "A wise judge shall judge his people." The first two are conditions for judging; but on the third the very rule of judgment is based, because the standard of judgment is the law of wisdom or truth, according to which the judgment is passed.
Now because the Son is Wisdom begotten, and Truth proceeding from the Father, and His perfect Image, consequently, judiciary power is properly attributed to the Son of God. Accordingly Augustine says (De Vera Relig. xxxi): "This is that unchangeable Truth, which is rightly styled the law of all arts, and the art of the Almighty Craftsman. But even as we and all rational souls judge aright of the things beneath us, so does He who alone is Truth itself pass judgment on us, when we cling to Him. But the Father judges Him not, for He is the Truth no less than Himself. Consequently, whatever the Father judges, He judges through It." Further on he concludes by saying: "Therefore the Father judges no man, but has given all judgment to the Son."
Reply to Objection 1. This argument proves that judiciary power is common to the entire Trinity, which is quite true: still by special appropriation such power is attributed to the Son, as stated above.
Reply to Objection 2. As Augustine says (De Trin. vi), eternity is attributed to the Father, because He is the Principle, which is implied in the idea of eternity. And in the same place Augustine says that the Son is the art of the Father. So, then, judiciary authority is attributed to the Father, inasmuch as He is the Principle of the Son, but the very rule of judgment is attributed to the Son who is the art and wisdom of the Father, so that as the Father does all things through the Son, inasmuch as the Son is His art, so He judges all things through the Son, inasmuch as the Son is His wisdom and truth. And this is implied by Daniel, when he says in the first passage that "the Ancient of days sat," and when he subsequently adds that the Son of Man "came even to the Ancient of days, who gave Him power, and glory, and a kingdom": and thereby we are given to understand that the authority for judging lies with the Father, from whom the Son received the power to judge.
Reply to Objection 3. As Augustine says (Tract. xcv in Joan.): "Christ said that the Holy Ghost shall convince the world of sin, as if to say 'He shall pour out charity upon your hearts.' For thus, when fear is driven away, you shall have freedom for convincing." Consequently, then, judgment is attributed to the Holy Ghost, not as regards the rule of judgment, but as regards man's desire to judge others aright.
Source: Summa Theologica (New Advent)