I am studying the book of Revelation. In Revelation 2:28, Jesus is talking to the church at Thyatira and he tells them that he will give them the morning star. What is the morning star? Also, there is a reference verse of II Peter 1:19 which talks about the day star. I am assuming that they are the same thing.
"And he who overcomes, and keeps My works until the end, to him I will give power over the nations -- 'He shall rule them with a rod of iron; They shall be dashed to pieces like the potter's vessels' -- as I also have received from My Father; and I will give him the morning star" (Revelation 2:26-28).
Jesus has received authority from the Father to reign. "Which He worked in Christ when He raised Him from the dead and seated Him at His right hand in the heavenly places, far above all principality and power and might and dominion, and every name that is named, not only in this age but also in that which is to come. And He put all things under His feet, and gave Him to be head over all things to the church, which is His body, the fullness of Him who fills all in all" (Ephesians 1:20-23). What Jesus is offering is that to those who overcome sin and remains faithful to the end, Jesus will give him the right to reign with him. See "The Christian's Reign" for more details.
"The Morning Star" is one of Jesus' titles. "I, Jesus, have sent My angel to testify to you these things in the churches. I am the Root and the Offspring of David, the Bright and Morning Star" (Revelation 22:16). Therefore, Jesus is offering also himself, or better yet fellowship with the Lord.
The morning star is what we now call Venus. It is a bright light that is easily seen during the dawn in various seasons. So yes, "And so we have the prophetic word confirmed, which you do well to heed as a light that shines in a dark place, until the day dawns and the morning star rises in your hearts" (II Peter 1:19). It can allude to the righteousness of Christ being seen in our lives because we have been changed by the Word. Though the direct reference in Peter is to a statement in Proverbs. "But the path of the just is like the shining sun, that shines ever brighter unto the perfect day" (Proverbs 4:18).