I maintain that the pressure at the center of the earth is zero. Matter there is subject to a uniform force field generated by the uniform distribution of matter around it. When I've discussed this with geology professors on my occasional college visits, they have either been speechless or asked if I would be interested in writing a paper. (I'm not, and my credentials are minimal. I am a non-academic with math degrees.)
ML/NJ
When the geology professor asked if you would be interested in writing a paper on the subject, that was the equivalent of a nice southern grandma saying “Why, bless your heart” : ),
We should build a space explorer for inner space and find out exactly what’s down there. A nuclear powered ball could slowly dig down for hundreds of years, and come back with gold and diamonds.
I doubt that gravitation there is null. It´s evidently the rotation of the inner core that gives rise to the magnetic field. Plus, even though it it is solid, if they´re right about the temperatures and pressures throughout, it must still be a very dynamic environment. Thus there would be no ¨center¨ in the way we usually conceive of it, but a constantly churning mass across it, from the classical to the quantum levels. And, it´s also subject to tidal forces of the Sun and Moon which constantly knead the entire Earth, and would also act to keep the ¨center¨ in a constant state of flux.
At the EXACT singularity center of the planet the gravity would be zero as all of the mass is 'above' you. The pressure would be still be immense. Equal and opposite pressures do not balance out; they double up.