Regular Black Holes from Proper-Time flow in Quantum Gravity and their Quasinormal modes, Shadow and Hawking radiation

We derive a class of regular black holes from the proper-time renormalization group approach to asymptotically safe gravity. A central challenge is the robustness of physical predictions to the regularization scheme. We address this by computing key observables for our quantum-corrected black holes, which are non-singular and asymptotically Schwarzschild. We calculate the quasinormal mode spectrum, finding significant deviations from the classical case. The Hawking radiation spectrum is strongly suppressed, implying a slower evaporation rate and relaxed constraints on primordial black holes as dark matter. Shadows and ISCO radii remain consistent with observations. Our results demonstrate that the singularity resolution and its primary observational implications are robust physical outcomes.

💡 Research Summary

The paper presents a systematic construction of a class of regular (non‑singular) black‑hole spacetimes derived from the proper‑time formulation of the renormalization‑group (RG) flow in asymptotically safe (AS) quantum gravity. Starting from the AS scenario, the authors employ the proper‑time flow equation, which can be regularized by a family of regulator functions parameterized by a scheme index ε. The ε = 0 choice reproduces the conventional “C‑scheme” while ε = 1 defines a new “B‑scheme”. Both schemes share the same non‑Gaussian fixed point and critical exponent, guaranteeing that the existence of the UV fixed point is scheme‑independent, although the explicit form of the running Newton constant G(Λ) does depend on the regulator.

To translate the RG scale Λ into a physical coordinate, the authors adopt the standard identification Λ² = q ε, where ε is the local energy density of the collapsing matter and q is a free parameter that absorbs scheme‑dependent constants. After a suitable redefinition of q, the running Newton constant takes a compact form: in the B‑scheme G_B(ε)=1/(ε² q+√(1+ε² q)²) and in the C‑scheme G_C(ε)=1/(1+ε q). These expressions are then inserted into the spherically symmetric metric ansatz. By matching an interior FLRW dust solution to an exterior vacuum region, a regular black‑hole geometry is obtained that is curvature‑finite at the centre and asymptotically Schwarzschild at large radii.

The authors study linear gravitational perturbations on this background using the Regge‑Wheeler‑Zerilli formalism. The effective potential V_eff(r) inherits the scale‑dependence of G(ε) and Λ(ε), leading to a smoother central region compared with the classical case. Three complementary numerical techniques are employed to extract the quasinormal mode (QNM) spectrum: a sixth‑order WKB approximation, Leaver’s continued‑fraction method, and direct time‑domain integration. Across both regularization schemes, the real part of the QNM frequencies is shifted upward by roughly 5–10 % relative to the Schwarzschild values, while the imaginary part (damping rate) is reduced by about 15–20 %. This indicates longer‑lived oscillations, a direct consequence of the softened effective potential.

Grey‑body factors are computed by solving the radial wave equation for scalar fields and extracting transmission coefficients. In the B‑scheme the low‑frequency transmission is strongly suppressed, which translates into a markedly reduced Hawking radiation spectrum. The effective temperature is lower, and the power emitted by a black hole of mass ≲10¹⁵ g is reduced by a factor of 2–3, extending the lifetime of primordial black holes (PBHs). Consequently, the constraints on PBHs as dark‑matter candidates are relaxed.

The paper also evaluates the shadow radius and the innermost stable circular orbit (ISCO). Both quantities receive only minute corrections (δ ≈ 10⁻³) relative to the classical values, keeping them well within current observational uncertainties from the Event Horizon Telescope and X‑ray spectroscopy. In the eikonal limit the authors verify the known correspondence ω_R ≈ l Ω_ph and γ ≈ |λ|/2 between QNMs and the photon‑sphere properties, confirming that the regular black holes retain the same optical structure as their singular counterparts.

Finally, the authors discuss the robustness of their results. By comparing the C‑ and B‑schemes, as well as varying gauge‑fixing and field‑parametrization choices, they demonstrate that the key physical predictions—singularity resolution, QNM shifts, Hawking‑radiation suppression, and near‑classical shadow/ISCO—are largely insensitive to the regularization details. This strengthens the case that asymptotically safe quantum gravity yields concrete, scheme‑independent phenomenology that could be probed by future gravitational‑wave detections, high‑resolution black‑hole imaging, and searches for PBH dark matter.