Effective Quantum Dust Collapse via Surface Matching

Abstract

The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validity of a static quantum black hole spacetime outside the collapsing matter, 2) homogeneity of the collapsing matter, and 3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model [1] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in-and outside observers can be answered.

Exteriors to bouncing collapse models

“…Another example for this behavior can also be found in Ref. [38], illustrated with the Penrose diagram in Fig. (14).…”

“…In Ref. [38], Fig. ( 14), a comparable Penrose diagram was found, although there the black hole and white hole blocks in the diagram are condensed into a single block with a transition surface in between, and no singularities are present.…”

“…The same class of static exteriors were investigated also in Ref. [38], where the discussion centered on specific loop quantum gravity models for the bounce. Here we aim to specifically illustrate aspects of dynamic exteriors, with horizons that expand and shrink.…”

Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model

“…As argued, this might be possible as L(t) becomes again arbitrarily large after a bounce. Usually, this happens in a parallel universe [38][39][40][41]51].…”

“…The mini-superspace model becomes a far more complicated proper field theory and the adaption of LQC techniques becomes more involved. Regardless, there is effort in understanding the more complicated black hole collapse in the context of effective LQG [28][29][30][31][32][33][34][35][36][37][38][39][40][41], but no consensus has emerged.…”