Nonexistence of quantum black and white hole horizons in an improved dynamic approach

In this paper, we study the quantum geometric effects near the locations where classical black hole horizons used to appear in Einstein’s classical theory, within the framework of an improved dynamic approach, in which the internal region of a black hole is modeled by the Kantowski-Sachs (KS) spacetime and the two polymerization parameters are functions of the phase space variables. Our detailed analysis shows that the effects are so strong that black and white hole horizons of the effective quantum theory do not exist at all and instead are replaced by transition surfaces, across which the metric coefficients and their inverses are smooth and remain finite, as are the corresponding curvatures, including the Kretschmann scalar. These surfaces always separate trapped regions from anti-trapped regions. The number of such surfaces is infinite, so the corresponding KS spacetimes become geodesically complete, and no black and white hole-like structures exist in this scheme.

Note:

revtex4-2, 6 figures, and two tables, v2: typos corrected, references added, v3: Additional analyses were provided, including new references and figures, while the conclusions remain the same, v4: to appear in SCIENCE CHINA Physics, Mechanics & Astronomy, v5: published version in SCIENCE CHINA Physics, Mechanics & Astronomy

canonical quantization
loop quantum gravity
quantum aspects of black holes
black hole: horizon
effect: geometrical
black hole: quantum
quantum gravity: loop space
space-time: Kantowski-Sachs
quantum geometry
quantization: polymer

References(67)

Figures(25)

[1]

The Large Scale Structure of Space-Time

S.W. Hawking
,
G.F.R. Ellis

[2]

Background independent quantum gravity: A Status report

Abhay Ashtekar
(
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)

- Class.Quant.Grav. 21 (2004) R53
•
e-Print:
- gr-qc/0404018
•
DOI:
- 10.1088/0264-9381/21/15/R01

[3]

Modern Canonical Quantum General Relativity

Thomas Thiemann
(
- Potsdam, Max Planck Inst.
)

DOI:
- 10.1017/CBO9780511755682

[4]

Absence of singularity in loop quantum cosmology

Martin Bojowald
(
- Penn State U.
)

- Phys.Rev.Lett. 86 (2001) 5227-5230
•
e-Print:
- gr-qc/0102069
•
DOI:
- 10.1103/PhysRevLett.86.5227

[5]

Isotropic loop quantum cosmology

Martin Bojowald
(
- Penn State U.
)

- Class.Quant.Grav. 19 (2002) 2717-2742
•
e-Print:
- gr-qc/0202077
•
DOI:
- 10.1088/0264-9381/19/10/313

[6]

Mathematical structure of loop quantum cosmology

Abhay Ashtekar
(
- Penn State U. and
- Schrodinger Inst., Vienna
)
,
Martin Bojowald
(
- Penn State U. and
- Schrodinger Inst., Vienna
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Schrodinger Inst., Vienna
)

- Adv.Theor.Math.Phys. 7 (2003) 2, 233-268
•
e-Print:
- gr-qc/0304074
•
DOI:
- 10.4310/ATMP.2003.v7.n2.a2

[7]

Quantum Nature of the Big Bang: Improved dynamics

- Phys.Rev.D 74 (2006) 084003
•
e-Print:
- gr-qc/0607039
•
DOI:
- 10.1103/PhysRevD.74.084003

[8]

Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field

Victor Taveras
(
- Penn State U.
)

- Phys.Rev.D 78 (2008) 064072
•
e-Print:
- 0807.3325
•
DOI:
- 10.1103/PhysRevD.78.064072

[9]

Loop Quantum Cosmology: A Status Report

Abhay Ashtekar
(
- Penn State U.
)
,
Parampreet Singh
(
- Louisiana State U.
)

- Class.Quant.Grav. 28 (2011) 213001
•
e-Print:
- 1108.0893
•
DOI:
- 10.1088/0264-9381/28/21/213001

[10]

Loop Quantum Cosmology: Physics of Singularity Resolution and Its Implications

Bao-Fei Li
(
- Zhejiang U. Tech. and
- Louisiana State U.
)
,
Parampreet Singh
(
- Louisiana State U.
)

[11]

Loop quantum cosmology: relation between theory and observations

e-Print:
- 2301.10215
•
DOI:
- 10.1007/978-981-19-3079-9_103-1

[12]

Dressed metric predictions revisited

- Class.Quant.Grav. 37 (2020) 9, 095001
•
e-Print:
- 1912.02556
•
DOI:
- 10.1088/1361-6382/ab7ee0

[13]

Are loop quantum cosmos never singular?

Parampreet Singh
(
- Perimeter Inst. Theor. Phys.
)

- Class.Quant.Grav. 26 (2009) 125005
•
e-Print:
- 0901.2750
•
DOI:
- 10.1088/0264-9381/26/12/125005

[14]

A Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

- Phys.Rev.D 80 (2009) 044024
•
e-Print:
- 0905.4949
•
DOI:
- 10.1103/PhysRevD.80.044024

[15]

Brief review on black hole loop quantization

Javier Olmedo
(
- Louisiana State U.
)

- Universe 2 (2016) 2, 12
•
e-Print:
- 1606.01429
•
DOI:
- 10.3390/universe2020012

[16]

Quantum extension of the Kruskal spacetime

- Phys.Rev.D 98 (2018) 12, 126003
•
e-Print:
- 1806.02406
•
DOI:
- 10.1103/PhysRevD.98.126003

[17]

Black Hole evaporation: A Perspective from Loop Quantum Gravity

Abhay Ashtekar
(
- Penn State U., University Park, IGC
)

- Universe 6 (2020) 2, 21
•
e-Print:
- 2001.08833
•
DOI:
- 10.3390/universe6020021

[18]

Quantum Geometry and Black Holes

- ,
- In: Bambi, C., Modesto, L., Shapiro, I. (eds) Handbook of Quantum Gravity. Springer, Singapore (2023)
•
e-Print:
- 2211.05621
•
DOI:
- 10.1007/978-981-19-3079-9_105-1