LTB spacetimes in terms of Dirac observables

Classical and Quantum Gravity

Volumn 27, Issue 10, 2010, Pages

  Giesel, Kristina ^a   Tambornino, Johannes ^b   Thiemann, Thomas ^b,c  

^a NORDITA   (Denmark)

^b ALBERT EINSTEIN INSTITUT   (Germany)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951606358     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/10/105013     Document Type: Article

References (35)

1. Arnowitt R, Deser S and Misner C 1962 The dynamics of general relativity Gravitation: An Introduction to Current Research ed L Witten (New York: Wiley) pp 227-65
2. Dirac P 1967 Lectures on Quantum Mechanics (New York: Yeshiva University)
3. Henneaux M and Teitelboim C 1992 Quantization of Gauge Systems (Princeton: Princeton University Press)
4. Bergmann P G 1961 'Gauge-invariant' variables in general relativity Phys. Rev. 124 274-78
5. Kuchar K V 1991 Time and interpretations of quantum gravity General Relativity and Relativistic Astrophysics Proceedings (Winnipeg) pp 211-314
6. Bergmann P G 1961 Observables in general relativity Rev. Mod. Phys. 33 510-4
7. Komar A 1958 Construction of a complete set of independent observables in the general theory of relativity Phys. Rev. 111 1182-87
8. Bergmann P G and Komar A B 1960 Poisson brackets between locally defined observables in general relativity Phys. Rev. Lett. 4 432-3
9. Rovelli C 1991 What is observable in classical and quantum gravity? Class. Quantum Grav. 8 297-316
10. Rovelli C 2002 Partial observables Phys. Rev. D 65 124013 (arXiv:gr-qc/0110035)
11. Vytheeswaran A 1994 Gauge unfixing in second class constrained systems Ann. Phys. 236 297
12. Dittrich B 2007 Partial and complete observables for Hamiltonian constrained systems Gen. Rel. Grav. 39 1891-927 (arXiv:gr-qc/0411013)
13. Dittrich B 2006 Partial and complete observables for canonical general relativity Class. Quantum Grav. 23 6155-84 (arXiv:gr-qc/0507106)
14. Dittrich B and Tambornino J 2007 A perturbative approach to Dirac observables and their space-time algebra Class. Quantum Grav. 24 757-84 (arXiv:gr-qc/0610060)
15. Dittrich B and Tambornino J 2007 Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology Class. Quantum Grav. 24 4543-86 (arXiv:gr-qc/0702093)
16. Thiemann T 2006 Reduced phase space quantization and Dirac observables Class. Quantum Grav. 23 1163-80 (arXiv:gr-qc/0411031)
17. Thiemann T 2006 Solving the problem of time in general relativity and cosmology with phantoms and k-essence arXiv:astro-ph/0607380
18. Brown J D and Kuchar K V 1995 Dust as a standard of space and time in canonical quantum gravity Phys. Rev. D 51 5600-29 (arXiv:gr-qc/9409001)
19. Giesel K, Hofmann S, Thiemann T and Winkler O 2010 Manifestly gauge-invariant general relativistic perturbation theory: I. Foundations Class. Quantum Grav. 27 055005 (arXiv:0711.0115 [gr-qc])
20. Giesel K, Hofmann S, Thiemann T and Winkler O 2010 Manifestly gauge-invariant general relativistic perturbation theory: II. FRW background and first order Class. Quantum Grav. 27 055006 (arXiv:0711.0117 [gr-qc])
21. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): IV. Reduced phase space quantisation of loop quantum gravity arXiv:0711.0119 [gr-qc]
22. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
23. Thiemann T 2007 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press)
24. Bondi H 1947 Spherically symmetrical models in general relativity Mon. Not. R. Astron. Soc. 107 410-25
25. Landau L and Lifshitz E 1987 The Classical Theory of Fields vol 2 4th edn (Oxford: Butterworth-Heinemann)
26. Szekeres P and Lun A 1999 What is a shell crossing singularity? J. Aust. Math. Soc. B 41 167-79
27. Lematre G 1933 L'univers en expansion Ann. Soc. Sci. Brux. A 53 51-85
28. Lasky P D, Lun A W C and Burston R B 2007 Initial value formalism for dust collapse ANZIAM J. 49 (arXiv:gr-qc/0606003)
29. Painlevé P 1921 La Mecanique classique et la theorie de la relativite C. R. Acad. Sci. (Paris) 173 677-80
30. Gullstrand A 1922 Allgemeine Lösung des statischen Einkörperproblems in der Einsteinschen Gravitationstheorie Arkiv. Mat. Astron. Fys. 16 1-15
31. Martel K and Poisson E 2001 Regular coordinate systems for Schwarzschild and other spherical spacetimes Am. J. Phys. 69 476-80 (arXiv:gr-qc/0001069)
32. Hellaby C and Lake K 1985 Shell crossings and the Tolman model Astrophys. J. 290 381
33. Grishchuk L and Zel'dovich Y B 1984 Structure and future of the new universe Mon. Not. R. Astron. Soc. 207 23-8
34. Beig R and Murchadha N 1987 The Poincaré group as the symmetry group of canonical general relativity Ann. Phys. (NY) 174 463-98
35. Tolman R C 1934 Effect of inhomogeneity on cosmological models Proc. Natl Acad. Sci. 20 169-76