Ultracompact horizonless objects in order-reduced semiclassical gravity

The backreaction of quantum fields in their vacuum state results in equilibrium structures that surpass the Buchdahl compactness limit. Such backreaction is encapsulated in the vacuum expectation value of the renormalized stress-energy tensor (RSET). In previous works we presented analytic approximations to the RSET, obtained by dimensional reduction, available in spherical symmetry, and showed that the backreaction-generated solutions described ultracompact fluid spheres with a negative mass interior. Here, we derive a novel approximation to the RSET that does not rely on dimensional reduction, but rather on a reduction of the differential order. This approximation also leads to regular stars surpassing the Buchdahl limit. We conclude that this is a consequence of the negative energies associated with the Boulware vacuum which, for sufficiently compact fluid spheres, make the Misner-Sharp mass negative near the centre of spherical symmetry. Our analysis provides further cumulative evidence that quantum vacuum polarization is capable of producing new forms of stellar equilibrium with robust properties accross different analytical approximations to the RSET.
Comment: 15 pages, 5 figures. Added a new figure, an appendix, and improved the main text. To appear in Phys. Rev. D