The study of regular black holes and black hole mimickers as alternatives to standard black holes has recently gained significant attention, driven both by the need to extend general relativity to describe black hole interiors, and by recent advances in observational technologies. Despite considerable progress in this field, significant challenges remain in identifying and characterizing physically well-motivated classes of regular black holes and black hole mimickers. This paper provides an overview of these challenges, and outlines some of the promising research directions — as discussed during a week-long focus program held at the Institute for Fundamental Physics of the Universe (IFPU) in Trieste from November 11th to 15th, 2024.

DOI: https://doi.org/10.1103/PhysRevLett.125.149002

We provide an exhaustive analysis of the complete set of solutions of the equations of stellar equilibrium under semiclassical effects. As classical matter we use a perfect fluid of constant density; as the semiclassical source we use the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field in the Boulware vacuum (the only vacuum consistent with asymptotic flatness and staticity). For the RSET we use a regularized version of the Polyakov approximation. We present a complete catalogue of the semiclassical self-consistent solutions which incorporates regular as well as singular solutions, showing that the semiclassical corrections are highly relevant in scenarios of high compactness. Semiclassical corrections allow the existence of ultracompact equilibrium configurations which have bounded pressures and masses up to a central core of Planckian radius, precisely where the regularized Polyakov approximation is not accurate. Our analysis strongly suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the regularized Polyakov approximation used here must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.

We present strong evidence that semiclassical gravity can give place to self-consistent ultracompact stars beyond the Buchdahl limit. We integrate the semiclassical equations of (spherically symmetric) stellar equilibrium for a constant-density classical fluid. The semiclassical contribution is modelled by a quantum massless scalar field in the only static vacuum state compatible with asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor (RSET) is firstly approximated by the analytic Polyakov approximation. This already reveals a crucial difference with respect to purely classical solutions: stars with compactness close to that of a black hole exhibit bounded pressures and curvatures up to a very small central core compared with the star radius. This suggests that a more refined approximation to the RSET at the core may give rise to strictly regular configurations. Following this suggestion, we prove that a minimal deformation of the Polyakov approximation inside the central core is sufficient to produce regular ultracompact stellar configurations.

We derive a master equation for the reduced density matrix of a uniformly accelerating quantum detector in arbitrary dimensions, generically coupled to a field initially in its vacuum state, and analyze its late time regime. We find that such density matrix asymptotically reaches a Gibbs state. The particularities of its evolution towards this state are encoded in the response function, which depends on the dimension, the properties of the fields, and the specific coupling to them. We also compare this situation with the thermalization of a static detector immersed in a thermal field state, pinpointing the differences between both scenarios. In particular, we analyze the role of the response function and its effect on the evolution of the detector towards equilibrium. Furthermore, we explore the consequences of the well-known statistics inversion of the response function of an Unruh-DeWitt detector linearly coupled to a free scalar field in odd spacetime dimensions. This allows us to specify in which sense accelerated detectors in Minkowski vacuum behave as static detectors in a thermal bath and in which sense they do not.

We investigate the effects of vacuum polarization on vacuum static spherically symmetric spacetimes. We start from the Polyakov approximation to the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field. This RSET is not regular at $r=0$, so we define a regularized version of the Polyakov RSET. Using this regularized RSET, and under the previous symmetry assumptions, we find all the solutions to the semiclassical field equations in vacuum. The resulting counterpart to the Schwarzschild classical geometry substitutes the presence of an event horizon by a wormhole throat that connects an external asymptotically flat region with an internal asymptotic region possessing a naked singularity: there are no semiclassical vacuum solutions with well-defined Cauchy surfaces. We also show that the regularized Polyakov RSET allows for wormhole geometries of arbitrarily small throat radius. This analysis paves the way to future investigations of proper stellar configurations with an internal nonvacuum region.