I'm a Christian and I believe the age of the Earth to be about 4.5 billion years old. On the other hand, I also believe the Earth to be about 6,000 years old. Both are correct if you see it in the perspective of General Relativity.
In order to understand this simple concept, we must gather the facts first.
Isaiah 42:5 - NIV
This is what God the Lord says-- he who created the heavens and stretched them out, who spread out the earth and all that comes out of it, who gives breath to its people, and life to those who walk on it:
Jeremiah 10:12 - NIV
But God made the earth by his power; he founded the world by his wisdom and stretched out the heavens by his understanding.
Jeremiah 51:15 - NIV
"He made the earth by his power; he founded the world by his wisdom and stretched out the heavens by his understanding.
Are these biblical verses scientifically factual? Is the Universe (the heavens) really expanding/stretching?
What does science says?
The Universe is stretching.
"Let me begin by saying that "expanding" isn't really the best word to describe what is happening to the universe, although that is the word that is often used - a word choice which I think leads to a lot of unnecessary confusion regarding what is already a difficult topic! A more accurate word for what the universe is doing might be "stretching"."
Source: Astronomy Department at Cornell University. (google the links as I can't post any links yet. I'm a new member.)
The biblical verses above are scientifically factual. God is behind the Big Bang where he created the universe out from a point of zero volume super black hole singularity and stretched them out to create the universe.
The Big Bang:
"According to the big bang theory, the universe began by expanding from an infinitesimal volume with extremely high density and temperature. The universe was initially significantly smaller than even a pore on your skin. With the big bang, the fabric of space itself began expanding like the surface of an inflating balloon – matter simply rode along the stretching space like dust on the balloon's surface. The big bang is not like an explosion of matter in otherwise empty space; rather, space itself began with the big bang and carried matter with it as it expanded."
Source: California Institute of Technology (google for the source)
Since God is the power behind the Big Bang, he must reside in a region of immense gravity in his omnipotent powers. He is the power behind black holes where super massive stars explode into a supernova and collapses into a black hole where no light can escape. The biblical verses below confirms this:
Joel 3 - RSV
15 The sun and the moon are darkened, and the stars withdraw their shining.
Jeremiah 4 - NIV
23 I looked at the earth, and it was formless and empty; and at the heavens, and their light was gone
Ezekiel 32 - NIV
7 When I snuff you out, I will cover the heavens and darken their stars;
Can stars withdraw their shining according to these verses? How?
In a Black Hole, light traveling outwards towards an event horizon is pulled back by the very strong gravitational field, because of the warping of space-time inside the event horizon, regardless of the lack of a photon mass. This prevents light from ever escaping the Black Hole.
Source : NASA (google the source)
A common type of black hole is the type produced by some dying stars. A star with a mass greater than 20 times the mass of our Sun may produce a black hole at the end of its life.
Source: Space Telescope Science Institute
Gathering all the facts, God is the power behind the 'Big Bang' and the stretching of the Universe. He is also the power behind Black Holes. In other words, God has the power of Gravity. The Biblical verses posted above and the scientific facts agrees with each other and are not in contradiction.
According to General Relativity, gravity itself can dilate time. Let say you are on a planet with 5x the gravity of the Earth. You will notice that the clock on planet Earth will tick faster than your clock. You read 12 noon on your clock, but on planet Earth, it's already 8pm in the evening.
Can God dilate time with his power of Gravity? According to this verse:
Peter 3:8 NIV
But do not forget this one thing, dear friends: With the Lord a day is like a thousand years, and a thousand years are like a day.
With God's power of gravity, he can dilate 1 day to 1 thousand years.
So, going back to the question: Is the Earth 6,000 years old? Was the Earth created in 6 days flat or 4.5 billion years?
Reading Genesis, we should see the creation relative to God and not to us in his perspective because he was the one who was there in the beginning. Relative to God with his immense power of gravity, all creation only took 6 days relative to Him. But, relative to us on Earth, time has already gone by in billions and billions of years.
I hope this clears things up a bit.