The fate of Reissner-Nordström-de Sitter black holes: nonequilibrium discharge and evaporation

A bstract We develop an analytic semiclassical effective model of Reissner-Nordström-de Sitter (RN-dS) discharge and evaporation by combining a spherically reduced two-dimensional description of the classical geometry with the pure Polyakov conformal sector for the radial energy flux. The framework captures the causal and thermodynamic structure of the static patch and yields closed adiabatic evolution equations for the mass and charge. With positive $$ \mathcal{F} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> the outward Killing-energy flux from the black-hole horizon to the cosmological horizon, the chosen Unruh-de Sitter state gives $$ \mathcal{F} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> = ( N eff /48 π )( $$ {\kappa}_b^2-{\kappa}_c^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>κ</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi>κ</mml:mi> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ), while the full mass evolution is Ṁ = − $$ \mathcal{F} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> + $$ {\Phi}_b\dot{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>̇</mml:mo> </mml:mover> </mml:math> , with Φ b = Q / r b . Along the sub-Nariai neutral Schwarzschild-de Sitter branch the ordering κ b &gt; κ c implies monotonic mass loss. Standard Schwinger pair production provides the discharge channel. In the rapid-discharge regime, charged trajectories become effectively neutral on a timescale short compared with the Polyakov-driven 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 Polyakov heat flux. Once discharge is included, the electromagnetic work term tilts the coupled effective vector field away from this curve. Thus the lukewarm locus is not an invariant trajectory of the coupled ( M , Q ) flow. When light charged species provide a rapid-discharge channel, the distinguished classical loci — cold/extremal, charged Nariai, ultracold, and lukewarm — are not attractors for controlled nondegenerate trajectories within this effective Polyakov-Schwinger model. These results give an adiabatically backreacted description of RN-dS evaporation in the specified two-dimensional regime and provide the semiclassical background for generalized-second-law monotonicity and conservative island/QES estimates.