We explore the hypothesis that the endpoint of black hole evaporation is a stable topological remnant—specifically, an axionic wormhole that preserves unitarity by storing the information originally contained in the black hole. We first review a two-dimensional Callan-Giddings-Harvey-Strominger (CGHS) toy model augmented with a topological dilaton coupling, which illustrates how a remnant with finite entropy can emerge as the end state of evaporation. We then turn to four dimensions and construct an effective field theory in which an axion field couples to the gravitational Pontryagin density. We present the correct modified Einstein equations and the axion equation of motion, and we derive the conserved Noether current associated with the shift symmetry for a massless axion. We show that static, spherically symmetric configurations with an axion vortex of winding number n admit a conserved integer topological charge. Motivated by known wormhole solutions in the literature, we discuss the possibility that such configurations correspond to regular, asymptotically flat bubble geometries. We compute the ADM mass of these objects and discuss the expected scaling Mᵣem ~ n MP³ / fₐ. The entropy of the remnant is analyzed from both the Euclidean on-shell action and topological considerations; while the microscopic counting remains an open problem, we argue that a topological contribution Sᵣem = 2π n arises naturally in certain string-theoretic completions. We compute the Euclidean instanton action that would mediate a transition from a black hole to a wormhole and show, within a thin-wall approximation, that it becomes of order unity when the black hole mass approaches the Planck scale, suggesting that unitarity is preserved. In the regime fₐ ≪ MP, the remnant mass ranges from grams to tons, making it a viable cold dark matter candidate. We discuss observational signatures including gravitational birefringence from the Chern-Simons coupling and a stochastic gravitational wave background from primordial black hole evaporation. Finally, we outline a numerical shooting method that could be used to construct explicit wormhole solutions and discuss the limitations of the current analysis.
Luca Eliseo Pavesi (Thu,) studied this question.