Quantum Tunneling of Primordial Black Holes to White Holes: Rates, Constraints, and Implications for Fast Radio Bursts

TL;DR

This paper investigates the rates of primordial black hole tunneling to white holes and their potential connection to fast radio bursts, finding that current observations do not support a dominant white-hole origin for FRBs.

Contribution

It provides a detailed rate calculation for PBH white-hole tunneling events considering various physical constraints and assesses their viability as FRB sources.

Findings

FRB-level rates occur only in restricted parameter regions.

Current observations are consistent with a subdominant white-hole contribution.

A dominant white-hole origin for FRBs is strongly disfavored.

Abstract

We calculate the present-day and cosmological volumetric rate of primordial black hole (PBH) quantum tunneling events to white holes, incorporating the competition between Hawking evaporation and tunneling, cosmological depletion, realistic mass-dependent abundance constraints, extended mass functions, and the alternative memory-burden scenario. The burst rate is maximized along a narrow ridge in the mass--tunneling-parameter plane where the effective PBH lifetime is comparable to the age of the Universe. Within the canonical Planck-star range of tunneling timescales, FRB-level rates arise only in two highly restricted regions: a low-mass window near the evaporation boundary, and a narrow sequential window where evaporation precedes tunneling; broadening the PBH mass function does not qualitatively alter this conclusion. We further assess observational constraints from FRB repetition statistics, radio spectral properties, prompt and diffuse gamma-ray limits, host-galaxy demographics, and gravitational-wave signatures. All current observations are consistent with a subdominant white-hole contribution to the FRB population but strongly disfavor a dominant origin. The rate calculation does not generically support FRB-level event densities, and any viable FRB interpretation requires narrow, fine-tuned, and strongly assumption-dependent corners of parameter space.