Quantum geometry and the Schwarzschild singularity

Classical and Quantum Gravity

Volumn 23, Issue 2, 2006, Pages 391-411

  Ashtekar, Abhay ^a,b,c   Bojowald, Martin ^a,b,c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b ALBERT EINSTEIN INSTITUT   (Germany)

^c ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31644445995     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/23/2/008     Document Type: Article

References (49)

1. Misner C W 1972 Minisuperspaces Magic Without Magic, John A Wheeler Festschrift ed J R Klauder (San Francisco: Freeman)
2. Hartle J B 1995 Spacetime quantum mechanics and the quantum mechanics of spacetime Gravitation and Quantizations: Proc. 1992 Les Houches Summer School (Amsterdam: North-Holland) (Preprint gr-qc/9304006)
3. Hartle J B and Hawking S W 1983 The wavefunction of the universe Phys. Rev. D 28 2960-75
4. Ashtekar A and Lewandowski L 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53-R152
5. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
6. Thiemann T 2004 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press) at press (Preprint gr-qc/0110034)
7. Bojowald M 2001 Absence of singularity in loop quantum cosmology Phys. Rev. Lett. 86 5227-30
8. Bojowald M 2003 Homogeneous loop quantum cosmology Class. Quantum Grav. 20 2595-615
9. Ashtekar A, Bojowald M and Lewandowski J 2003 Mathematical structure of loop quantum cosmology Adv. Theor. Math. Phys. 7 233-68
10. Ashtekar A, Pawlowski T and Singh P 2005 Quantum nature of the big bang: an analytical and numerical study in preparation
11. Dafermos M 2003 Black hole formation from a complete regular past Preprint gr-qc/0310040
12. Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
13. Horowitz G T and Myers R 1995 The value of singularities Gen. Rel. Grav. 27 915-9
14. Marolf D 1995 Refined algebraic quantization: systems with a single constraint Preprint gr-qc/9508015
15. Giulini N and Marolf D 1999 On the generality of refined algebraic quantization Class. Quantum Grav. 16 2479-88
16. Giulini N and Marolf D 1999 A uniqueness theorem for constraint quantization Class. Quantum Grav. 16 2489-505
17. Ashtekar A and Bojowald M 2005 Black hole evaporation: a paradigm Class. Quantum Grav. 22 3349-62
18. Stevens C R, 't Hooft G and Whiting B F 1994 Black hole evaporation without information loss Class. Quantum Grav. 11 621-48
19. Hayward S 2005 The disinformation problem for black holes (conference version) Preprint gr-qc/0504038
20. Modesto L 2004 The Kantowski-Sachs space-time in loop quantum gravity Preprint gr-qc/0411032
21. Kobayashi S and Nomizu K 1963 Foundations of Differential Geometry (New York: Wiley)
22. Brodbeck O 1996 On symmetric gauge fields for arbitrary gauge and symmetry groups Helv. Phys. Acta 69 321-4
23. Bojowald M and Kastrup H A 2000 Symmetry reduction for quantized diffeomorphism invariant theories of connections Class. Quantum Grav. 17 3009-43
24. Ashtekar A and Samuel J 1991 Bianchi cosmologies: the role of spatial topology Class. Quantum Grav. 8 2191-215
25. Kastrup H A and Thiemann T 1994 Spherically symmetric gravity as a completely integrable system Nucl. Phys. B 425 665-86
26. Kuchař K V 1994 Geometrodynamics of Schwarzschild black holes Phys. Rev. D 50 3961-81
27. Thiemann T 1996 Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity Phys. Lett. B 380 257-64
28. Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quantum Grav. 15 839-73
29. Thiemann T 1998 QSD V: quantum gravity as the natural regulator of matter quantum field theories Class. Quantum Grav. 15 1281-314
30. Ashtekar A, Fairhurst S and Willis J 2003 Quantum gravity, shadow states, and quantum mechanics Class. Quantum Grav. 20 1031-62
31. Willis J 2004 On the low-energy ramifications and a mathematical extension of loop quantum gravity PhD Dissertation Pennsylvania State University
32. Bojowald M 2001 Inverse scale factor in isotropic quantum geometry Phys. Rev. D 64 084018
33. Bojowald M 2005 Degenerate configurations, singularities and the non-Abelian nature of loop quantum gravity Preprint gr-qc/0508118
34. Brunnemann J and Thiemann T 2005 Unboundedness of triad-like operators in loop quantum gravity Preprint gr-qc/0505033
35. Husain V and Winkler O 2004 Quantum resolution of black hole singularities Class. Quantum Grav. 22 L127-34
36. Dasgupta A 2005 Semiclassical quantisation of space-times with apparent horizons Preprint gr-qc/0505017
37. Bojowald M, Date G and Vandersloot K 2004 Homogeneous loop quantum cosmology: the role of the spin connection Class. Quantum Grav. 21 1253-78
38. Bojowald M and Date G 2004 Consistency conditions for fundamentally discrete theories Class. Quantum Grav. 21 121-43
39. Bojowald M 2002 Isotropic loop quantum cosmology Class. Quantum Grav. 19 2717-41
40. Ashtekar A, Bojowald M and Willis J 2005 Modifications to Friedmann's equation from quantum geometry in preparation
41. Bojowald M 2001 The semiclassical limit of loop quantum cosmology Class. Quantum Grav. 18 L109-L116
42. Bojowald M 2001 Dynamical initial conditions in quantum cosmology Phys. Rev. Lett. 87 121301
43. Cartin D and Khanna G 2005 Absence of pre-classical solutions in Bianchi I loop quantum cosmology Phys. Rev. Lett. 94 111302
44. Date G 2005 Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology Phys. Rev. D 72 067301
45. Ashtekar A, Pawlowski T and Singh P 2005 Closed cosmology and quantum geometry in preparation
46. Bojowald M 2004 Spherically symmetric quantum geometry: states and basic operators Class. Quantum Grav. 21 3733-53
47. Bojowald M and Swiderski R 2004 The volume operator in spherically symmetric quantum geometry Class. Quantum Grav. 21 4881-900
48. Bojowald M and Swiderski R 2005 Spherically symmetric quantum geometry: Hamiltonian constraint Preprint gr-qc/0511108
49. Bojowald M 2005 Non-singular black holes and degrees of freedom in quantum gravity Phys. Rev. Lett. 95 061301