Modelling the Evaporation of Non-singular Black Holes

TL;DR

This paper develops a model for the formation and evaporation of non-singular black holes, incorporating quantum corrections and radiation back-reaction, enabling numerical studies of their complete dynamical spacetimes.

Contribution

It introduces a generalized action-based model with equations of motion suitable for numerical analysis of non-singular black hole spacetimes with dynamical horizons.

Findings

Equations of motion derived in null and Painleve--Gullstrand coordinates.

Model preserves constraint algebra and energy-momentum conservation.

Provides a framework for studying black hole evaporation without singularities.

Abstract

We present a model for studying the formation and evaporation of non-singular (quantum corrected) black holes. The model is based on a generalized form of the dimensionally reduced, spherically symmetric Einstein--Hilbert action and includes a suitably generalized Polyakov action to provide a mechanism for radiation back-reaction. The equations of motion describing self-gravitating scalar field collapse are derived in local form both in null co--ordinates and in Painleve--Gullstrand (flat slice) co--ordinates. They provide the starting point for numerical studies of complete spacetimes containing dynamical horizons that bound a compact trapped region. Such spacetimes have been proposed in the past as solutions to the information loss problem because they possess neither an event horizon nor a singularity. Since the equations of motion in our model are derived from a diffeomorphism invariant action they preserve the constraint algebra and the resulting energy momentum tensor is manifestly conserved.