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I've tried googling for "Time dilation due to acceleration" but found nothing particular. Here when I entered title of the question the site have not shown same question asked already. Upon typing in the question the site found:

Gravitational Time Dilation vs Acceleration Time Dilation

Time dilation in a gravitational field and the equivalence principle

I've read those still do not see clear answer to my question(s) below.

In wikipedia for time dilation there are dilation due to relative speed and gravitational one. However as far as I've understood General relativity is based on "Einstein equivalence principle". And from the principle it follows that acceleration with 1g on a spaceship will be experienced same as gravitation on Earth surface. But what about time dilation on a ship accelerating 1g? (speed still small or accounted for separately if that is possible ...). If time dilation is the same due to equivalence, why then clock in the core of Earth will go even slower than surface whereas acceleration due to gravity = 0 in the core.

Martian2020
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  • Dude in the rocket is fooled to think that clocks there run at different rates. He gets fooled by the Doppler-shift of light. Dude at the center of earth is in a real gravity field. – stuffu Nov 01 '20 at 09:36
  • @stuffu, "fooled": I assume rocket returns to starting point to compare clock with one left at starting point. Does accelerations of 1g vs say 10g matters as for time dilation? I'm reading suggested QAs, one accepted answer says: "invariance of the line element." and then some math too complex for me (at least for now). – Martian2020 Nov 01 '20 at 16:08
  • Having gravitational potential energy causes a clock to tick faster. Having kinetic energy causes a clock to tick slower. There, that was the full and complete story. As you see, acceleration is not mentioned. – stuffu Nov 10 '20 at 18:26

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