Drop an ice cube into boiling water, and it will melt away until nothing is left. A black hole in space behaves much the same way — except the 'boiling water' is space itself, which continuously siphons energy out of the hole.
In the new work, physicists traced the fate of a special class of black holes: those that not only have mass but also carry an electric charge. Such holes are described by the Reissner–Nordström solution in de Sitter space (a model of a universe that expands at a constant rate). The authors included two key processes: quantum radiation that carries off energy, like water evaporating from a puddle, and particle pair production that gradually removes the charge, like static electricity draining from a charged comb.
The authors also checked whether special states, such as when the hole's temperature matches that of its surroundings, are stable. They found they are not: extra energy flowing in or out due to electromagnetic effects knocks the system off balance. So the classical 'rest points' do not survive once quantum corrections are included.
as written by the authors arXiv:2605.20349
We develop a semiclassical description of Reissner--Nordstr\"om--de Sitter (RN--dS) evaporation by combining a spherically reduced two-dimensional dilaton gravity model with Polyakov anomaly backreaction. The framework captures the causal and thermodynamic structure of the static patch and yields closed adiabatic evolution equations for the mass and charge. With an outward-oriented flux convention, the anomaly-induced Killing-energy flux is $$\mathcal F=(N_{\rm eff}/48\pi)(\kappa_b^2-\kappa_c^2)$$, while the full mass evolution is $$\dot M=-\mathcal F+\Phi_b\dot Q$$, with $$\Phi_b=Q/r_b$$. We prove analytically that along the entire sub-Nariai neutral Schwarzschild--de Sitter branch $$\kappa_b>\kappa_c$$, so neutral black holes lose mass monotonically. Schwinger pair production provides the discharge channel. In the rapid-discharge regime, controlled charged trajectories become effectively neutral on a timescale short compared with the anomaly-driven Hawking mass-loss time and then follow the neutral SdS channel toward empty de Sitter space. The classical lukewarm locus $$T_b=T_c$$ is only the nullcline of the anomaly-induced heat flux: the electromagnetic work term tilts the full semiclassical vector field away from this curve, so it is not an invariant trajectory. When sufficiently light charged species provide a rapid-discharge channel, the classical cold/extremal, charged Nariai, ultracold, and lukewarm loci are not semiclassical attractors for controlled nondegenerate trajectories. These results give an adiabatically backreacted derivation of the RN--dS evaporation endpoint in the regime controlled by anomaly-induced flux and rapid charge discharge, and provide the semiclassical background for generalized-second-law monotonicity and conservative quantum-extremal-surface/island estimates.
During evaporation, a black hole can reach a temperature at which it shines brighter than the surface of the Sun, but only for a very brief moment.