Breaking Buchdahl: ultracompact stars in semiclassical gravity
The semiclassical approximation takes into account the gravitational contribution of zero-point energies. We model this contribution via the renormalized stress-energy tensor (RSET) of a massless scalar field, which we compute in a cutoff-regularized version of the Polyakov approximation. When the field is in the Boulware vacuum state (the natural vacuum for stellar geometries), the RSET works in favor of violating the Buchdahl compactness limit. We review the family of classical constant-density stellar solutions, paying particular attention to the notion of criticality -- the presence of offsets in the mass function -- and use it as a warm up for the analysis of the semiclassical set of solutions. For stars that surpass Buchdahl limit by far, the critical solution has an irregular pressure. This divergence in pressure moves inward by introducing a negative offset in the mass. In the semiclassical theory we find something rather different, namely that the critical configuration already displays a pressure that diverges exactly at the center of the structure. This drastic difference between the classical and semiclassical space of solutions suggests that semiclassical gravity could potentially allow for the existence of ultracompact stellar objects.