Black Core

Clays have an element of organic matter in them, which should burn out during the bisque firing. If this doesn't happen, and it occurs during the glaze firing, then gasses will be given off. If the outer part of the clay body has softened and become impervious, then the pressure of the gas will cause bloating, with bumps forming on the surface of the clay. Or, if the gas can escape from the clay, and the glaze has melted, it may form bubbles that could either stay trapped in the glaze, or leave imperfections on the glaze surface.
Often this is visible if you break the pot after bisque firing, and the clay in the centre is dark grey to black from unburnt or part burnt organic matter.
Most organic matter is burned out by about 650°C, but the thicker the clay, the longer the time that must be allowed for this, as it takes longer for the clay to heat through.

Solution

Don't fire too fast from the start of the bisque firing up to 650°C, or include a hold at the top of this temperature range. This will allow the full thickness of the clay to heat up and burn out any organic matter. Thicker clay will require a longer time. Also, clay with a high organic content - an indication of this is if the clay is dark grey coming out of the bag, but a much lighter colour after firing.