What would happen if earths core collapsed in on itself

Hello :)

My first hypothesis: If the Earth's core were to collapse on itself the pressure and heat would cause the core to cool and eventually the Earth would cool off and not be able to sustain life.

My second hypothesis: The earth would explode

Due to the unique nature of this question, I wasn't quite sure what the answer was, so I gave two hypotheses. Hope these give some insight :)

Answerthe global climate during the paleogene departed from the hot and humid conditions of the late mesozoic era and began a cooling and drying trend which dispite having been periodically disrupted by warm periods such as the paleocene-eocene thermal maximum, persists today;