Breaking Buchdahl: Ultracompact stars in semiclassical gravity

Abstract

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 perturbative 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.

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

“…In [63], the authors construct solutions where the final state of the collapse occurs at infinite time t, where t corresponds to the temporal foliation (the physically preferred foliation) of a distant observer. The use of semi-classical gravity is done in [64,65], taking into account the vacuum expectation value of a regularization of the stress-energy tensor. The authors show that the back-reaction generates solutions describing ultra-compact fluid spheres with a negative mass interior, leading to regular static stars with mass M and radius R surpassing the Buchdahl limit M < 32π 9 RM 2 pl .…”

How Much Cosmic Time Does It Take for a Star to Collapse Forming a Black Hole?

“…In [53], the authors construct solutions where the final state of the collapse occurs at infinite time t, where t corresponds to the temporal foliation (the physically preferred foliation) of a distant observer. The use of semi-classical gravity is done in [54,55], taking into account the vacuum expectation value of a regularization of the stress-energy tensor. The authors show that the back-reaction generates solutions describing ultra-compact fluid spheres with a negative mass interior, leading to regular static stars with mass M and radius R surpassing the Buchdahl limit M < 32π 9 RM 2 pl .…”