In realtiy no object can have a solid core, as gravity is always stronger on the outside of a object than at the center. in cases where there is a soild middle such as a rock it is the weakest point within the rock.
A simple lesson in the distribution of mass will show you right from wrong. if you slice a piece of pie you will always find that the larger piece of pie is one the out side not on the inside.
another simple lesson is to look at a people that stand on the world, on one side a person stands on the world, just as well a person stands on the opposite side of the world, they both are held to the ground, there for gravity has changed the direction of its pull, and at the center of the earth must switch, as gravity must switch for two people to satnd on opposite sides of the world, the two must pull at the center of the earth leaving a vacant space.
A small sun like object at the center of the earth is debatable, but inorder to produce a magnetic feild ionzation at least must occur, and so you have to figure out does that cause enough electricall conduction to be a small sun. some people think the center of the earth is a nuclear reactor.
i hope this helps a little bit.
DwayneD.L.Rabon