Ultra‐compact objects in semiclassical gravity

In this investigation, we study the structure of ultra‐compact stars in the framework of semiclassical gravity , an extension of Einstein's general relativity (GR), in which a classical spacetime metric is coupled to the quantum expectation value of the stress tensor and that incorporates the polarization of the quantum vacuum in the presence of a gravitational field. In this approach, a generalization of the classical Tolman–Oppenheimer–Volkoff (TOV) equations may be derived. Unlike most theoretical treatments based on GR, this formulation allows a wider range of consistent equation of state (EoS) solutions with enough compactness to produce a photon sphere without violating the Buchdahl limit, an upper bound on the compactness, thus motivating future studies to investigate if ultra‐compact stars could act as black hole mimickers . The main novelty of this extended formalism, when compared to the conventional form of the TOV equations, is the presence of an additional repulsive term—due to quantum corrections originated by the phenomenon of quantum vacuum polarization —that can withstand, under certain conditions, the gravitational collapse. Although the quantum corrections furnished by semiclassical gravity are negligible in most compact stars scenarios, for ultra‐compact configurations, where the star radius is not much larger than its gravitational radius, such effects may be relevant.