Interestingly, the pressure inside the star is outward and any object inside the star moves outward. The fact that is confirmed by simulations and experiments. Now, assume that there is a brush and a star interpenetrating each other slightly. This problem is strictly hard because the star is spherically symmetric and brush is planary symmetric. To guess the most probable grand potential functional of this system, we must choose between cartesean and spherical polar coordinates. I think its more convenient to choose the cartesean coordinate system. So the grand potential functional is written as follows,