Coherent electrically-charged quantum black holes

TL;DR

This paper refines the quantum-corrected Reissner–Nordström geometry within the coherent-state framework by implementing a Gaussian UV regulator, removing unphysical oscillations and yielding a metric with $f(r)=1-rac{R_M}{r} ext{erf}igl( frac{r}{R_s}igr)+rac{R_Q^2}{r^2}rac{2r}{R_s} ext{F}igl( frac{r}{R_s}igr)$. The resulting spacetime is sourced by an anisotropic effective stress-energy tensor and exhibits a richer causal structure, including regimes with two, one, or no horizons, and a possible regular origin when $R_s=R_s^*$. Geodesic observables (photon sphere, lensing, Shapiro delay) and scalar quasinormal modes show deviations from classical RN that grow with the core size, with QNMs displaying longer lifetimes while preserving the qualitative frequency characteristics, supporting a regularization-independent qualitative picture of quantum-corrected black holes with potential implications for UV completions and stability.

Abstract

We improve upon the results presented in [R. Casadio, et al., Phys. Rev. D 105 (2022) 124026] deriving a quantum-corrected Reissner-Nordström geometry containing an integrable singularity at its center while being devoid of spurious oscillations around the classical configuration. We further investigate some relevant physical observables, related to geodesics and quasinormal modes of scalar perturbations, associated with this geometry to complement our theoretical analysis.

Figures (5)

• Figure 1: Metric function $f(r)=1+2V^{\rm q}_{\rm RN}(r)$ for different values of the parameters $R_{\rm s}$ and $R_{\rm Q}$ (in units of $R_{\rm M}$).
• Figure 2: Left: normalized effective energy density (solid line) and tangential pressure (dashed line) for $R_{\rm s}/R_{\rm M}=0.3$ and $R_{\rm Q}/R_{\rm M}=0.1$. Right: normalized mass function for $R_{\rm s}/R_{\rm M}=0.1$.
• Figure 3: Number of solutions to the equation $V_{\rm RN}^{\rm q}(r)=-1/2$, or equivalently $f(r)=0$, in the parameter space $R_{\rm s}$--$R_{\rm Q}$ (in units of $R_{\rm M}$). Inside the elliptical dark gray region, the equation $f(r)=0$ has one solution with multiplicity one; while on the dark gray boundary between the light gray region (two solutions) and the black region (no solutions), $f(r)=0$ admits one solution with multiplicity two, corresponding to the extremal case.
• Figure 4: Left: (outer) photon radius $R_\gamma$ (in units of $R_{\rm M}$) as a function of $R_{\rm s}/R_{\rm M}$. Right: critical impact parameter $b_{\rm c}$ (in units of $R_{\rm M}$) as a function of $R_{\rm s}/R_{\rm M}$. For both plots we have chosen to depict two values of $R_{\rm Q}/R_{\rm M}$, and we always compare their quantum-corrected values to the corresponding classical RN cases ($R_{\rm s}\to0^+$).
• Figure 5: Left: $\Delta\phi_{\rm d}$ as a function of $R_{\rm s}/R_{\rm M}$. Right: Shapiro time delay $\Delta t_{\rm d}/R_{\rm M}$ as a function of $R_{\rm s}/R_{\rm M}$ where, for simplicity, we have taken $r_{A}=r_{B}=2r_0$, $r_0$ being the radius associated to $b$. For both plots we have chosen two values of $R_{\rm Q}/R_{\rm M}$ with $b=2R_{\rm M}$. Moreover, we have depicted in gray the vertical asymptotes corresponding to the maximum values of $R_{\rm s}$, for which $b=b_{\rm c}$. It is also worth noting that the values of the observables for the RN case are represented by the horizontal asymptotes approached by the curves as $R_{\rm s} \to 0^+$.