TY - JOUR

T1 - Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

AU - Andrianov, Alexander A.

AU - Starodubtsev , Artem

AU - Elmahalawy, Yasser

N1 - Andrianov, A.A.; Starodubtsev, A.; Elmahalawy, Y. Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell. Universe 2020, 6, 201.

PY - 2020

Y1 - 2020

N2 - We perform Hamiltonian reduction of a model in which 2 + 1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of ADS2—both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of ADS2 momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

AB - We perform Hamiltonian reduction of a model in which 2 + 1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of ADS2—both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of ADS2 momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

KW - quantum gravity

KW - thin shell

KW - BTZ black hole

KW - singularity avoidance

UR - https://www.mdpi.com/2218-1997/6/11/201

M3 - Article

VL - 6

JO - Universe

JF - Universe

SN - 2218-1997

IS - 11

M1 - 201

ER -