Quantum-Corrected Bondi Mass for 2D Hawking Radiation

Abstract

We derive the Hamiltonian for general semi-classical 2D dilaton gravity, beginning with the complete action including the Polyakov action and Gibbons-Hawking-York boundary term. The value of the Hamiltonian yields a generalized Brown-York quasi-local mass function, and the ADM and Bondi masses are obtained in the appropriate limits. The Bondi mass is equal to the classical mass plus a correction term given by the transformation between initial and final inertial frames. It is non-increasing and remains positive in numerical simulations.

Figures (1)

• Figure 1: The Bondi mass and its decomposition into a classical part ($\mathcal{M}_{DG}$) and quantum correction ($\mathcal{M}_P$) for two semi-classical evaporating black hole spacetimes. Details of the models and the numerical methods used are available in BarenboimEtAlEvaporationRegular2025. Top: A Schwarzschild black hole with $M=1, \mu=1$. The simulation ends at the last ray where the horizon and singularity meet and the final Bondi mass converges to a positive value. Bottom: A Bardeen black hole with $M=0.7, \mu=6$. In this case the simulation ends when the collapsing matter that generates the black hole reaches $r=0$; the solution after this point will depend on the boundary conditions imposed here. The oscillations in the classical mass are related to transitions between trapped and anti-trapped regions.