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 Bodendorfer et al (2019 Class. Quantum Grav. 36 195015) 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.

Quantum corrected polymer black hole thermodynamics: mass relations and logarithmic entropy correction

“…Note that the present analysis based on [1,2] together with the methods described in [104][105][106][107] would in principle allow to construct an effective picture of the full collapse and evaporation process of a quantum black hole. Again, it would be important to analyze the quantum theory first, to see the range of validity of the effective picture.…”

The End of a Black Hole's Evaporation -- Part II

“…The existence of a classical solution of the Einstein field equations describing a spacetime in which the exterior of a past black hole and a future white hole are connected [1] indicates that the end of the evaporation of a black hole can result in a quantum tunnelling from a trapped to an anti-trapped region. The black to white hole transition is receiving increasing attention in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14]. In [15], following the scenario developed in [16][17][18][19][20][21][22][23][24][25], we have introduced a technique to study this transition.…”

Group quantization of the black hole minisuperspace

“…Despite the large effort, for the black hole dynamics no agreement has been found yet [17][18][19][20][21][22][23][24][25][37][38][39][40][41][42][43]. Moreover, the majority of the works about black hole dynamics start directly by the heuristic effective dynamics introducing by hand the polymer correction.…”