There are several serious theoretical difficulties with the solid shell variant of the Dyson sphere:
Such a shell would have no net gravitational interaction with its englobed star (see shell theorem), and could drift in relation to the central star. If such movements went uncorrected, they could eventually result in a collision between the sphere and the starmost likely with disastrous results. Such structures would need either some form of propulsion to counteract any drift, or some way to repel the surface of the sphere away from the star.
For the same reason, such a shell would have no net gravitational interaction with anything else inside it. The contents of any biosphere placed on the inner surface of a Dyson shell would not be attracted to the sphere's surface and would simply fall into the star. It has been proposed that a biosphere could be contained between two concentric spheres, placed on the interior of a rotating sphere (in which case, the force of artificial "gravity" is perpendicular to the axis of rotation, causing all matter placed on the interior of the sphere to pool around the equator, effectively rendering the sphere a Niven ring for purposes of habitation, but still fully effective as a radiant-energy collector) or placed on the outside of the sphere where it would be held in place by the star's gravity. In such cases, some form of illumination would have to be devised, or the sphere made at least partly transparent, because the star's light would otherwise be completely hidden.
