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Ref. There is a ‘gravity hole’ in the Indian Ocean, and scientists now think they know why

According to CNN, the 'gravity hole' is an area of decreased gravity, compared with the surroundings. This article says that the lower gravity causes to sea level to locally fall (~100m). It seems to me that if there is less gravity at the 'hole' relative to the surroundings, the surrounding higher gravity would cause the sea level to rise up in a swelling over the hole, whilst pulling down the sea all around the hole. Just as the Moon's gravity pulls the seas towards it.

So why does the sea go down rather than up?

Paul Uszak
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This is because regions with higher gravity attract ocean water drawing it away from regions with lower gravity, leaving less water and lower sea level in the lower gravity regions.

Higher gravity regions can't "pull down" the water because water is almost incompressible and there is no place "down" for the water to go. The water just piles up over high gravity regions.

This reminds me of the Greenland sea level paradox: If all the ice in Greenland melted, the local sea level around Greenland would actually drop because the Greenland ice cap is so massive it gravitationally attracts water into the North Atlantic raising local sea level.

David Bailey
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Images to graphically describe what I believe David Bailey's answer is explaining.

Gravity doesn't just pull down. It also pulls sideways. When gravity is equal everywhere, the vertical and horizontal components cancel out, for a flat surface.

Equal gravity has a flat surface.

When gravity is unequal, there's less vertical pressure on the water, but there's also less force pulling inwards. So the high-gravity areas around the low-gravity area are able to pull the water sideways, away from the low-gravity area.

Unequal gravity has a not flat surface.

More images to graphically describe what I believe user253751'a answer is explaining.

Water follows an imaginary surface of equal gravitational potential. Imagine two different sources of gravity with different strengths. Both objects will have strong (red) gravity closer, and medium (orange) and light (yellow) gravity further out. But the radius at which the high gravity object pulls with a given strength is farther away from the center of the object.

Dense object has potential farther out.

If we move the objects close together, their gravitational fields merge.

Objects near each other mix their fields.

Gravity is additive, so the fields smooth each other out where they connect.

Merged gravity fields are smoother.

Water follows the gravity field at some level. In this case, I drew it slightly farther than "light" gravity, but in reality it will be whatever level has enough volume beneath it to hold all the water.

Water with dip because of merged gravity fields having unlevel potential height.

MichaelS
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(Based on David's answer but maybe a bit more intuitive - this is how I understood it)

The sea level is a surface of constant gravitational potential. Otherwise the water flows from higher to lower potential.

In parts of the world with weaker gravity, the gravitational potential is less at the same height, which means the same gravitational potential exists at a lower height in these places.

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I think it's helpful to use thought experiments trying to imagine extreme cases and what would happen.

In this case, imagine the Western hemisphere was solid earth, and the Eastern hemisphere was replaced with a hollow shell with vacuum inside and smooth on the outside, but with the water from the Eastern hemisphere still roughly in place. I would naturally expect all the water from the Eastern hemisphere to flow around the hollow shell towards the Western hemisphere because the gravity of the Western hemisphere would attract it. This would lead to shallower water in what was the Indian ocean.