TY  - JOUR
AU  - Beltran-Palau, P.
AU  - del Rio, A.
AU  - Navarro-Salas, J.
PY  - 2023
DA  - 2023//
TI  - Quantum corrections to the Schwarzschild metric from vacuum polarization
T2  - Phys. Rev. D
JO  - Physical Review D
SP  - 085023
EP  - 15pp
VL  - 107
IS  - 8
PB  - Amer Physical Soc
AB  - We explore static and spherically symmetric solutions of the 4-dimensional semiclassical Einstein's equations using the quantum vacuum polarization of a conformal field as a source. These solutions may be of interest for the study of exotic compact objects (ECOs). The full backreaction problem is addressed by solving the semiclassical Tolman-Oppenheimer-Volkoff (TOV) equations making use of effective equations of state inspired by the trace anomaly and an extra simplifying and reasonable assumption. We combine analytical and numerical techniques to solve the resulting differential equations, both perturbatively and nonperturbatively in h. In all cases the solution is similar to the Schwarzschild metric up p ffiffito the vicinity of the classical horizon r = 2M. However, at r = 2M + epsilon, with epsilon similar to O(root h), we find a coordinate singularity. In the case of matching with a static star, this leads to an upper bound in the compactness, and sets a constraint on the family of stable ECOs. We also study the corrections that the quantum-vacuum polarization induces on the propagation of waves, and discuss the implications. For the pure vacuum case, we can further extend the solution by using appropriate coordinates until we reach another singular point, where this time a null curvature singularity arises and prevents extending beyond. This picture qualitatively agrees with the results obtained in the effective two-dimensional approach, and reinforces the latter as a reasonable method.
SN  - 2470-0010
UR  - https://arxiv.org/abs/2212.08089
UR  - https://doi.org/10.1103/PhysRevD.107.085023
DO  - 10.1103/PhysRevD.107.085023
LA  - English
N1  - WOS:000988649200017
ID  - Beltran-Palau_etal2023
ER  -