For all atmospheric games (excepting trace anthropogenic gases) "room temperature" (never mind core temperature) is above the critical temperature. Thus a liquid phase cannot exist although the system can be supercritical above the critical pressure. The nonzero pressure is as noted in the post to which I'm responding, but stated differently, is a function of asymmetry. Even though the gravitational acceleration at the center point appears to approach zero, the gas is compressed by the apparent "weight" of the gas above it.
The Earth, I believe, is not massive enough to create sufficient pressure for solidifying common atmospheric games but if I correctly recall the large gas giants are, and can in fact induce multiple solid phases, for instance, metallic hydrogen.
I believe some of these pressures have been experimentally observed using devices like diamond anvils. I seem to recall this was a topic discussed by Raold Hoffman in a lecture I attended many years ago on the topic of extreme pressures.
One may intuitively gain insight to this question of whether the pressure is zero at the center of a gas object by asking if Jupiter is hollow.
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