There is no obstacle to gravitational action on the Sun's core. In one of the great mysteries of the cosmos, everything appears to be totally transparent to gravity.

What Ray is asking is about the possibility that the gravitational acceleration of the Sun's hot core might be different from that of a cold object, for relativistic reasons. I would yield to current experts on general relativity to analyze that one.

I see no merit to the angular momentum idea, for reasons I have expressed in prior threads.