TL;DR, the ocean level would barely change with the elimination of Lulisia, even if the hole went to the center of the earth. I was wrong. Oda was also wrong.
Here is what AI has to say:
Based on the principles of displacement and the fact that sea ice already floating in the ocean does not change the sea level when it melts, it would suggest that making a hole in the ocean that extends to the center of the Earth would not change the sea level. This is because the volume of water displaced by the hole would be equal to the volume of the hole itself.
However, this is an oversimplification of a very complex set of physical systems, and several factors could cause the actual outcome to be different. For example, seawater isn't just water - it's a solution of various salts and other substances, so the specific gravity and density come into play. Additionally, the question assumes the hole remains vacant - and doesn't consider potential seepage of matter from the Earth's interior - magma, for instance.
Furthermore, this explanation doesn't consider the Earth's gravitational field, geopotential masks, and tides, which all contribute to the actual sea level at any given point. One interesting consideration is the pronounced dip in the geoid (the hypothetical shape the ocean surface would take under the influence of gravity alone if other influences such as winds and tides were absent) under the Indian Ocean called the Indian Ocean geoid low (IOGL). This is an area where Earth's gravity is lower than average, causing the sea level to be significantly lower than the global average.
Lastly, it's important to remember that real-world phenomena often don't behave as simply as conceptual models might predict. Environmental, gravitational, and other factors make this an extremely complex issue. In reality, creating a hole to the center of the Earth poses significant scientific and logistical challenges and uncertainties, and it could have unforeseen consequences on Earth's geology and climate.
Pt 2, with considerations of gravitational fields, etc.:
The issue really becomes quite complex when we consider the gravitational effects as the hole approaches the center of the Earth. If the hole is indeed reaching to the center of the Earth, and assuming it's somehow possible to maintain this hole without it collapsing under the immense pressure and heat, the gravitational effects would be significant.
As you go deeper into the Earth, the gravitational force you experience decreases because the mass beneath you becomes less. The force due to gravity at a particular point inside the Earth depends on the amount of mass beneath that point. If you were at the very center of the Earth, you would experience zero gravity because you would be completely surrounded by Earth's mass and it would pull you equally in all directions.
If we now imagine a body of water being subject to this gravitational field - as in your hypothetical ocean hole - the water near the surface of the hole will experience roughly Earth's surface gravity (neglecting additional mass from water), while water further down the hole will experience progressively less gravity.
The water in the hole would thus adopt a sort of pressure gradient where the water at the top is being pulled down by gravity and the water at the bottom experiences less gravitational pull. This could result in a change in sea level that deviates from the simple displacement assumption.
However, it's important to note that this is a very theoretical exercise, and it's fraught with assumptions that do not reflect real-world conditions. The temperature and pressure conditions, together with the shifts in the Earth's gravitational field, would cause such a hole to rapidly collapse long before it could reach the center of the earth. Not to mention the geological and climate effects that drilling such a hole would have on Earth. This kind of experiment is beyond our current scientific and technological capabilities and poses significant risks.
Didn’t we literally just have a break?
