Disclaimer

I am not sure whether this question belongs here or in the Physics SE but I'm posting here due to the fictionnal aspect of the celestial body.

Context

I'm writing a story where humans discover a small planet-sized celestial body they name Eurarch. After investigation, they discover Eurarch has a core located in one of its extremity where the density is about 2.5 times greater than anywhere else in the planet.

They manage to land and establish a colony on the opposite extremity, where the gravitationnal pull is the weakest. An expedition is sent to travel through months to the densest extremity of Eurarch and, as the gravity seems to goes stronger and stronger, they finally reach their destination.

They discover that Eurarch dense core is an artificial construct and part of it manages to expel whatever ending up too close to the core to the other extremity of the planet, thus keeping the dense artificial core at one extremity.

Problematic

The gravitation of Eurarch is one of the key point of my story and I would like to know if a celestial body where the gravity goes stronger as you travel toward the "core" is possible ? If so, I'm almost sure it cannot be a globe but I cannot figure out what its shape would be ?