At every point in the sphere the force vector due to gravity is the sum of all force vectors acting on it. At the center are all the vectors add up to 0. Is this correct?
They have to add up to zero.
So if we built a Dyson sphere with the mass of a black hole, at the diameter of an event horizon, would we still have a black hole? Would the sum of the gravity in the center of that artificial black hole be zero?
Hydrostatic vs shear stress.
A submarine that goes deeper than it’s rated depth shall implode, but not because of the difference in pressure between the upper and lower portions of the hull, but because the outside forces are greater than what the hull can resist.
For every force there is an equal and opposite force for systems in equilibrium, but nothing says the egg shaped earth has an equilibrium without dynamic changes in such a model. If the forces cancel each other at the center, this just means the center isn’t moving, but is in equilibrium.
If all the gravitational forces are acting upon each other, there might not be an acceleration, but the hydrostatic stress on that small volume still will be tremendous.
I thought the model of the interior core was one of a plasma.