Analytical and numerical study of a microscopic black hole reactor: Hawking evaporation, Bondi accretion, and stability analysis.

Can a fixed surrounding medium balance the mass loss of a microscopic black hole? We combine idealized Bondi accretion with a blackbody approximation to Hawking emission, then analyze the resulting mass equation. We find a single positive balance, but a small change in mass drives the system away from it. An exact implicit solution and numerical trajectories show how the evolution differs near and far from the balance. For an illustrative water-like choice of parameters, the reference black hole evaporates rapidly in the blackbody model, while departures from a nearly balanced state can be slow. This instability is an exact property of the fixed-coefficient equation, not a general impossibility result for black hole energy systems. Continuum accretion, realistic emission spectra and environmental feedback require separate treatment. Full source code, notebooks, and reproducibility materials are available in the linked GitHub repository.