At the end of the book of Revelation, the apostle John sees a) a great white throne, b) a Person sitting on it whose presence earth and heaven fled, and c) the judgment of the dead from things written in a number of books, including the Book of life, according to their deeds.

Then I saw a great white throne and Him who sat upon it, from whose presence earth and heaven fled, and no place was found for them. And I saw the dead, the great and the small, standing before the throne, and books were opened; and another book was opened, which is the book of life; and the dead were judged from the things which were written in the books, according to their deeds. And the sea gave up the dead who were in it, and Death and Hades gave up the dead who were in them; and they were judged, each one of them according to their deeds. (Rev 20:11-13)

The New Testament has not portrayed Jesus Christ as a fearsome Person whose presence earth and heaven would flee. Is this Person on the Great White Throne Jesus Christ the eschatological King / Judge or perhaps God?

There is good evidence that Jesus Christ is indeed the One sitting on the Great White Throne.

To Jews who sought to kill Him, Jesus states that all judgment, in the context of eschatological judgment, was given to Him by His Father:

For the Father loves the Son and shows Him all things that He Himself is doing; and the Father will show Him greater works than these, so that you will be amazed. For just as the Father raises the dead and gives them life, so the Son also gives life to whom He wishes. For not even the Father judges anyone, but He has given all judgment to the Son, so that all will honor the Son just as they honor the Father. The one who does not honor the Son does not honor the Father who sent Him. Truly, truly, I say to you, the one who hears My word, and believes Him who sent Me, has eternal life, and does not come into judgment, but has passed out of death into life. (John 5:20-24)

To His disciples, Jesus tells them that He will sit on His glorious throne, which sounds like the Great White Throne, actively judging the twelve tribes of Israel and all the nations gathered before Him:

And Jesus said to them, "Truly I say to you, that you who have followed Me, in the regeneration when the Son of Man will sit on His glorious throne, you also shall sit upon twelve thrones, judging the twelve tribes of Israel. (Matt 19:28)

But when the Son of Man comes in His glory, and all the angels with Him, then He will sit on His glorious throne. And all the nations will be gathered before Him; and He will separate them from one another, just as the shepherd separates the sheep from the goats; and He will put the sheep on His right, but the goats on the left. (Matt 25:31-33)

To the public, Jesus tells them what judgment is based on and how He is involved:

"Not everyone who says to Me, 'Lord, Lord,' will enter the kingdom of heaven, but the one who does the will of My Father who is in heaven will enter. Many will say to Me on that day, 'Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?' And then I will declare to them, 'I never knew you; leave Me, you who practice lawlessness.' (Matt 7:21-23)

However, has all the evidence surrounding this event been considered? When writing in the context of the eschatological judgment of Believers, the apostle Paul speaks of the judgment seat of God (Greek: bēma theos) synonymously as the judgment seat of Christ (Greek: bēma christos):

But as for you, why do you judge your brother or sister? Or you as well, why do you regard your brother or sister with contempt? For we will all appear before the judgment seat of God (Greek: bēma theos). For it is written:
"As I live, says the Lord, to Me every knee will bow,
And every tongue will give praise to God."
So then each one of us will give an account of himself to God. (Rom 14:10-12)

For we must all appear before the judgment seat of Christ (Greek: bēma christos), so that each one may receive compensation for his deeds done through the body, in accordance with what he has done, whether good or bad. (2 Cor 5:10)

Paul leaves the impression that the eschatological judgment of everyone involves both God and His Son Jesus. John records only one moment in which eschatological judgment occurs (Rev 20:11-13), which suggests Paul's judgment seat of God / Christ is associated with John's Great White Throne.

Investigating this further, who has the cosmic power and presence that would cause earth and heaven to flee?

God.

Although Jesus was involved, God is attributed as the Creator:

In the beginning God created the heavens and the earth (Gen 1:1). This is the account of the heavens and the earth when they were created, in the day that the Lord God made earth and heaven (Gen 2:4).

Both the king of Salem, priest of the most high God, Melchizedek and Abram recognized God as the possessor of heaven and earth:

And he blessed him and said, "Blessed be Abram of God Most High, Possessor of heaven and earth; (Gen 14:19)

But Abram said to the king of Sodom, "I have sworn to the Lord God Most High, Possessor of heaven and earth, (Gen 14:22)

The prophet Isaiah speaks of God creating new heavens and a new earth:

For behold, I create new heavens and a new earth; And the former things will not be remembered or come to mind. (Isa 65:17)

Jesus Christ.

Jesus indicates that all authority in heaven and on earth has been given to Him:

And when they saw Him, they worshiped Him; but some were doubtful. And Jesus came up and spoke to them, saying, "All authority in heaven and on earth has been given to Me. Go, therefore, and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, (Matt 28:17-19)

Both God and His Son.

The apostle Peter speaks of the Day of the Lord and the Day of God as synonyms in which heaven and earth are destroyed:

But the day of the Lord will come like a thief, in which the heavens will pass away with a roar and the elements will be destroyed with intense heat, and the earth and its works will be discovered. Since all these things are to be destroyed in this way, what sort of people ought you to be in holy conduct and godliness, looking for and hastening the coming of the day of God, because of which the heavens will be destroyed by burning, and the elements will melt with intense heat! But according to His promise we are looking for new heavens and a new earth, in which righteousness dwells. (1 Pet 3:10-13)

The biblical evidence appears to support the view that God is present during the judgment of all the nations gathered before Him presided by His Son Jesus Christ. While both are associated with the Great White Throne, John sees only one Person sitting on the throne. Despite the difficulty of understanding this, just as the concept of a triune God, there is an illustration of something similar revealed in New Jerusalem.

As John witnesses a new heaven and a new earth, he sees the holy city New Jerusalem coming out of heaven from God. Within it, he observes that the temple in New Jerusalem is the Lord God the Almighty and the Lamb.

I saw no temple in it, for the Lord God the Almighty and the Lamb are its temple. And the city has no need of the sun or of the moon to shine on it, for the glory of God has illuminated it, and its lamp is the Lamb. (Rev 21:22-23)

It seems plausible that, in similar fashion, there is some sort of dual occupancy of the Great White Throne.

Because of the presence of millions of sinners during this judgment, the Great White Throne is not likely located in holy Temple of God (third heaven) and instead likely located in the vicinity of the Lake of Fire (outside of third heaven).

When Jesus speaks of His "glorious" throne (Matt 19:28; 25:31-33), is this mention of glory a reference to His Father being the throne?

Having both God and His Son present at the Great White Throne would certainly cause earth and heaven to flee and be destroyed.

While this is simply a hypothesis, it does provide a reasonable concept, coherent within the context of the whole Bible, that helps one understand all the available biblical data.