The spherically symmetric Standard Model with gravity

General Relativity and Gravitation

Volumn 37, Issue 8, 2005, Pages 1435-1482

  Balasin, H ^a   Bohmer C G ^a   Grumiller, D ^a,b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

2d theories; Dilaton gravity; Spherical symmetry; Standard Model

Indexed keywords

EID: 24944557204     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10714-005-0128-6     Document Type: Review

References (117)

1. Frolov, V.P., Novikov, I.D.: Black hole physics: Basic concepts and new developments. Dordrecht, Netherlands: Kluwer Academic (1998)
2. Efthimiou, C.J., Spector, D.A.: A collection of exercises in two-dimensional physics. I [hep-th/0003190]
3. Krasnov, K., Solodukhin, S.N.: Effective stringy description of Schwarzschild black holes, [hep-th/0403046]
4. Hooft, G.'t: The black hole interpretation of string theory. Nucl. Phys. B 335, 138-154 (1990)
5. Bojowald, M., Swiderski, R.: Spherically symmetric quantum horizons [gr-qc/0410147]
6. Husain, V., Winkler, O.: Quantum black holes [gr-qc/0412039]
7. Ashtekar, A. et al.: Isolated horizons and their applications. Phys. Rev. Lett. 85, 3564-3567 (2000) [gr-qc/0006006]
8. Fischer, P., Grumiller, D., Kummer, W., Vassilevich, D.V.: S-matrix for s-wave gravitational scattering. Phys. Lett. B 521, 357-363 (2001) [gr-qc/0105034] Erratum ibid. B 532, 373 (2002)
9. Grumiller, D.: Virtual black holes and the S-matrix [hep-th/0409231]
10. 't Hooft, G.: The scattering matrix approach for the quantum black hole: An overview. Int. J. Mod. Phys. A 11, 4623-4688 (1996) [gr-qc/9607022]
11. Choptuik, M.W.: Universality and scaling in gravitational collapse of a massless scalar field. Phys. Rev. Lett. 70, 9-12 (1993)
12. Gundlach, C.: Critical phenomena in gravitational collapse. Phys. Rept. 376, 339-405 (2003) [gr-qc/0210101]
13. Weinberg, S.: A model of leptons. Phys. Rev. Lett. 19, 1264-1266 (1967)
14. Davoudiasl, H., Kitano, R., Li, T., Murayama, H.: The new minimal standard model [hep-ph/0405097]
15. Fels, M.E., Torre, C.G.: The principle of symmetric criticality in general relativity. Class. Quant. Grav. 19, 641-676 (2002) [gr-qc/0108033]
16. Palais, R.: The principle of symmetric criticality. Commun. Math. Phys. 69, 19-30 (1979)
17. Deser, S., Tekin, B.: Shortcuts to high symmetry solutions in gravitational theories. Class. Quant. Grav. 20, 4877-4884 (2003) [gr-qc/0306114]
18. Ivey, TA., Landsberg, J.M.: Cartan for beginners: Differential Geometry via Moving frames and Exterior Differential Systems. AMS, Providence (2003)
19. 4-theory of gravity in the teleparallelism limit. Phys. Lett. B 94, 44-49 (1980)
20. Grumiller, D., Kummer, W., Vassilevich, D.V.: Dilaton gravity in two dimensions. Phys. Rept. 369, 327-429 (2002) [hep-th/0204253]
21. Hehl, F.W.: Spin and torsion in general relativity: I. Foundations. Gen. Rel. Grav. 4, 333-349 (1973);
22. Spin and torsion in general relativity: II. Geometry and field equations. Gen. Rel. Grav. 4, 491-516 (1974);
23. Hehl, F.W., Von Der Heyde, P., Kerlick, G.D., Nester, J.M.: General relativity with spin and torsion: Foundations and prospects. Rev. Mod. Phys. 48, 393-416 (1976)
24. Alimohammadi, M., Shariati, A.: Neutrino oscillation in a space-time with torsion. Mod. Phys. Lett. A 14, 267-274 (1999) [gr-qc/9808066];
25. Hammond, R.T.: Torsion gravity. Rept. Prog. Phys. 65, 599-649 (2002);
26. Hehl, F.W., McCrea, J.D., Mielke, E.W., Neeman, Y.: Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rept. 258, 1-171 (1995) [arXiv:gr-qc/9402012];
27. Hayashi, K., Sasaki, R.: Spinor electrodynamics in the Riemann-Cartan space and dynamical theory of axial - vector torsion propagating in vacuum. Nuovo Cim. B 45, 205-228 (1978)
28. Berger, B.K., Chitre, D.M., Moncrief, V.E., Nutku, Y.: Hamiltonian formulation of spherically symmetric gravitational fields. Phys. Rev. D 5, 2467-2470 (1972);
29. Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870 (1976);
30. Benguria, R., Cordero, P., Teitelboim, C.: Aspects of the Hamiltonian dynamics of interacting gravitational gauge and Higgs fields with applications to spherical symmetry. Nucl. Phys. B 122, 61 (1977);
31. Thomi, P., Isaak, B., Hájíček, P.: Spherically symmetric systems of fields and black holes. 1. Definition and properties of apparent horizon. Phys. Rev. D 30, 1168 (1984);
32. Hájíček, P.: Spherically symmetric systems of fields and black holes. 2. Apparent horizon in canonical formalism. Phys. Rev. D 30, 1178 (1984);
33. Mignemi, S., Wiltshire, D.L.: Spherically symmetric solutions in dimensionally reduced space-times. Class. Quant. Grav. 6, 987 (1989);
34. Thiemann, T., Kastrup, H.A.: Canonical quantization of spherically symmetric gravity in Ashtekar's selfdual representation. Nucl. Phys. B 399, 211-258 (1993) [arXiv:gr-qc/9310012];
35. Kastrup, H.A., Thiemann, T.: Spherically symmetric gravity as a completely integrable system. Nucl. Phys. B 425, 665-686 (1994) [arXiv:gr-qc/9401032];
36. Kuchař, K.V.: Geometrodynamics of Schwarzschild black holes. Phys. Rev. D 50, 3961-3981 (1994) [arXiv:gr-qc/9403003];
37. Lau, S.R.: On the canonical reduction of spherically symmetric gravity. Class. Quant. Grav. 13, 1541-1570 (1996) [arXiv:gr-qc/9508028]
38. Grumiller, D., Kummer, W.: Absolute conservation law for black holes. Phys. Rev. D 61, 064006 (2000) [gr-qc/9902074]
39. Schmidt, H.-J.: The classical solutions of two-dimensional gravity. Gen. Rel. Grav. 31 1187-1210 (1999) [gr-qc/9905051]
40. Obukhov, Y.N., Hehl, F. W.: Black holes in two dimensions [hep-th/9807101]
41. Schaller, P., Strobl, T.: Poisson structure induced (topological) field theories. Mod. Phys. Lett. A 9, 3129-3136 (1994) [hep-th/9405110]
42. Klösch, T., Strobl, T.: Classical and quantum gravity in (1+1)-dimensions. Part I: A unifying approach. Class. Quant. Grav. 13, 965-984 (1996) [arXiv:gr-qc/9508020];
43. Classical and quantum gravity in 1+1 dimensions. Part II: The universal coverings. Class. Quant. Grav. 13, 2395-2422 (1996) [arXiv:gr-qc/9511081];
44. Classical and quantum gravity in 1+1 dimensions. Part III: Solutions of arbitrary topology and kinks in 1+1 gravity. Class. Quant. Grav. 14, 1689-1723 (1997) [hep-th/9607226];
45. A global view of kinks in 1+1 gravity. Phys. Rev. D 57, 1034-1044 (1998) [arXiv:gr-qc/9707053]
46. Israel, W.: New interpretation of the extended Schwarzschild manifold. Phys. Rev. 143, 1016 (1966)
47. Zaslavsky, O.B.: Semi-infinite throats at finite temperature and static solutions in exactly solvable models of 2d dilaton gravity. Phys. Lett. B 459, 105-111 (1999) [hep-th/9904184]
48. Bronnikov, K.A., Melnikov, V.N.: Conformal frames and d-dimensional gravity, in The gravitational constant: Generalized gravitational theories and experiments., de Sabbata, V., Gillies, G.T., Melnikov, V.N. (eds).: NATO Advanced Study Institute, 18th course of the international school of gravitation and cosmology, May 2003. Kluwer (2004) [gr-qc/0310112]
49. Grumiller, D., Mayerhofer, D.: On static solutions in 2d dilaton gravity with scalar matter. Class. Quant. Grav. 21, 5893-5914 (2004) [gr-qc/0404013]
50. Schutz, B.F.: Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle. Phys. Rev. D 2, 2762-2773 (1970)
51. Rahman, S., Visser, M.: Spacetime geometry of static fluid spheres. Class. Quant. Grav. 19, 935-952 (2002) [gr-qc/0103065]
52. Mann, R.B.: Conservation laws and 2-d black holes in dilaton gravity. Phys. Rev. D 47, 4438-4442 (1993) [hep-th/9206044]
53. Buchdahl, H.: Phys. Rev. 111, 1417 (1959)
54. Gergely, L.A.: Spherically symmetric static solution for colliding null dust. Phys. Rev. D 58, 084030 (1998) [gr-qc/9809024]
55. Grumiller, D.: Three functions in dilaton gravity: The good, the bad and the muggy, in Proceedings of International Workshop on Mathematical Theories and their Applications, Moskaliuk, S. (ed.): pp. 59-96, TIMPANI. Cernivtsi, Ukraine (2004) [hep-th/0305073]
56. Rendall, A.D., Schmidt, B.G.: Existence and properties of spherically symmetric static fluid bodies with a given equation of state. Class. Quant. Grav. 8, 985-1000 (1991)
57. Baumgarte, T.W., Rendall, A.D.: Regularity of spherically symmetric static solutions of the Einstein equations. Class. Quant. Grav. 10 327-332 (1993)
58. Mars, M., Martin-Prats, M.M., Senovilla, J.M.M.: The 2m <= r property of spherically symmetric static spacetimes. Phys. Lett. A 218, 147-150 (1996) [gr-qc/0202003]
59. Tolman, R.C.: Static solutions of Einstein's field equations for spheres of fluid. Phys. Rev. 55, 364-373 (1939)
60. Oppenheimer, J.R., Volkoff, G.M.: On massive neutron cores. Phys. Rev. 55, 374-381 (1939)
61. Geroch, R., Held, A., Penrose, R.: A space-time calculus based on pairs of null directions. J. Math. Phys. 14, 874-881 (1973)
62. Penrose, R., Rindler, W.: Spinors and Space-Time I. Cambridge University Press (1984)
63. Gubser, S.S.: Absorption of photons and fermions by black holes in four dimensions. Phys. Rev. D 56, 7854-7868 (1997) [hep-th/9706100]
64. Godina, M., Matteucci, P., Fatibene, L., Francaviglia, M.: Two-spinor formulation of first order gravity coupled to Dirac fields. Gen. Rel. Grav. 32, 145-160 (2000) [gr-qc/9903023]
65. Dirac, P.A.M.: The quantum theory of the electron. Proc. Roy. Soc. A117, 610-624 (1928);
66. The quantum theory of the electron, Part II. Proc. Roy. Soc. A 118, 351-361 (1928);
67. Penrose, R.: The mathematics of the electron's spin. Eur. J. Phys. 18, 164-168 (1997)
68. Goldberg, J.N., MacFarlane, A.J., Newman, E.T., Rohrlich, F., Sudarshan, E.C.G.: Spin s spherical harmonics and edth. J. Math. Phys. 8, 2155 (1967)
69. Witten, E.: Some exact multipseudoparticle solutions of classical Yang- Mills theory. Phys. Rev. Lett. 38, 121 (1977)
70. Forgács, P., Manton, N.S.: Space-time symmetries in gauge theories. Commun. Math. Phys. 72, 15 (1980)
71. Volkov, M.S., Gal'tsov, D.V.: Gravitating non-Abelian solitons and black holes with Yang-Mills fields. Phys. Rept. 319, 1-83 (1999) [hep-th/9810070]
72. Corrigan, E., Olive, D.I., Fairlie, D.B., Nuyts, J.: Magnetic monopoles in SU(3) gauge theories. Nucl. Phys. B 106, 475 (1976)
73. Gal'tsov, D.V., Volkov, M.S.: Charged nonabelian SU(3) Einstein Yang-Mills black holes. Phys. Lett. B 274, 173-178 (1992)
74. Klinkhamer, F.R., Lee, Y.J.: Spectral flow of chiral fermions in nondissipative gauge field backgrounds. Phys. Rev. D 64 065024 (2001) [hep-th/0104096];
75. New analytic results for electroweak baryon number violation hep-th/0110237;
76. Yaffe, L.G.: Static solutions of SU(2) Higgs theory. Phys. Rev. D 40, 3463 (1989)
77. Ratra, B., Yaffe, L.G.: Spherically symmetric classical solutions in SU(2) gauge theory with a Higgs field. Phys. Lett. B 205 57, (1988)
78. Rudolph, G., Tok, T., Volobuev, I.: Exact solutions in Einstein-Yang-Mills-Dirac systems. J. Math. Phys. 40, 5890-5904 (1999) [gr-qc/9707060]
79. Greene, B.R., Mathur, S.D., O'Neill, C.M.: Eluding the no hair conjecture: Black holes in spontaneously broken gauge theories. Phys. Rev. D 47, 2242-2259 (1993) [hep-th/9211007]
80. Mondaini, R.P., Santos, N.O.: Conformally flat Einstein Yang-Mills Higgs solutions with spherical symmetry. Phys. Rev. D 28, 1872-1875 (1983)
81. Hawking, S.W.: Interacting quantum fields around a black hole. Commun. Math. Phys. 80, 421 (1981)
82. Page, D.N.: Thermal stress tensors in static einstein spaces. Phys. Rev. D 25, 1499 (1982)
83. Zecca, A.: The Dirac equation in the Newman-Penrose formalism with torsion. Nuovo Cim. B 117, 197-201 (2002);
84. Dirac equation in space-time with torsion. Int. J. Theor. Phys. 41, 421-428 (2002)
85. Griffiths, J.B.: Neutrino fields in Einstein-Cartan theory. Gen. Rel. Grav. 13, 227-237 (1981)
86. Thirring, W.E.: A soluble relativistic field theory. Annals Phys. 3, 91-112 (1958)
87. Griffiths, J.B., Jogia, S.: A Newman-Penrose-Type Formalism for Space-Times with Torsion. Gen. Rel. Grav. 12, 597-617 (1980)
88. Weyssenhoff, J., Raabe, A.: Relativistic dynamics of spin-fluids and spin-particles. Acta Phys. Pol. IX, 7-18 (1947)
89. Griffiths, J.B., Jogia, S.: A Spin-Coefficient Approch to Weyssenhoff Fluids in Einstein-Cartan Theory. Gen. Rel. Grav. 14, 137-149 (1982)
90. Böhmer, C.G.: The Einstein static universe with torsion and the sign problem of the cosmological constant. Class. Quant. Grav. 21, 1119-1124 (2004) [gr-qc/0310058]
91. Hojman, R., Mukku, C., Sayed, W.A.: Parity violation in metric torsion theories of gravitation. Phys. Rev. D 22, 1915-1921 (1980)
92. Weinberg, S.: Gravitation and cosmology. John Wiley & Sons (1972)
93. Frolov, V., Sutton, P., Zelnikov, A.: The dimensional-reduction anomaly. Phys. Rev. D 61, 024021 (2000) [hep-th/9909086];
94. Nojiri, S., Odintsov, S.D.: Anomaly induced effective actions in even dimensions and reliability of s-wave approximation. Phys. Lett. B 463, 57-62 (1999) [hep-th/9904146];
95. Sutton, P.: The dimensional-reduction anomaly in spherically symmetric spacetimes. Phys. Rev. D 62, 044033 (2000) [hep-th/0003290];
96. Balbinot, R., Fabbri, A., Frolov, V., Nicolini, P., Sutton, P., Zelnikov, A.: Vacuum polarization in the Schwarzschild spacetime and dimensional reduction. Phys. Rev. D 63, 084029 (2001) [hep-th/0012048];
97. Cognola, G., Zerbini, S.: On the dimensional reduction procedure. Nucl. Phys. B 602, 383-398 (2001) [hep-th/0008061]
98. Bartnik, R., Mckinnon, J.: Particle-like solutions of the Einstein Yang-Mills equations. Phys. Rev. Lett. 61, 141-144 (1988)
99. Torii, T., Maeda, K.-i., Tachizawa, T.: Cosmic colored black holes. Phys. Rev. D 52, 4272-4276 (1995) [gr-qc/9506018];
100. Volkov, M.S., Straumann, N., Lavrelashvili, G.V., Heusler, M., Brodbeck, O.: Cosmological analogues of the Bartnik-McKinnon solutions. Phys. Rev. D 54, 7243-7251 (1996) [hep-th/9605089]
101. Tolksdorf, J.: The Einstein-Hilbert-Yang-Mills-Higgs action and the Dirac-Yukawa operator. J. Math. Phys. 39, 2213-2241 (1998) [hep-th/9612149]
102. Walker, M.: Block diagrams and the extension of timelike two-surfaces. J. Math. Phys. 11 2280 (1970)
103. Birrell, N.D., Davies, P.C.W.: Quantum fields in curved space. Cambridge, Uk: Univ. Pr. 340p. (1982)
104. Kummer, W., Liebl, H., Vassilevich, D.V.: Integrating geometry in general 2d dilaton gravity with matter. Nucl. Phys. B 544 403-431 (1999) [hep-th/9809168];
105. Grumiller, D., Kummer, W., Vassilevich, D.V.: The virtual black hole in 2d quantum gravity. Nucl. Phys. B 580, 438-456 (2000) [gr-qc/0001038];
106. Grumiller, D.: Quantum dilaton gravity in two dimensions with matter. PhD thesis, Technische Universität Wien (2001) [gr-qc/0105078];
107. The virtual black hole in 2D quantum gravity and its relevance for the S-matrix. Int. J. Mod. Phys. A 17, 989-992 (2001) [hep-th/0111138];
108. Virtual black hole phenomenology from 2d dilaton theories. Class. Quant. Grav. 19, 997-1009 (2002) [gr-qc/0111097];
109. Grumiller, D., Kummer, W., Vassilevich, D.V.: Virtual black holes in generalized dilaton theories (and their special role in string gravity). European Phys. J. C 30 135-143 (2003) [hep-th/0208052];
110. Positive specific heat of the quantum corrected dilaton black hole. JHEP 07, 009 (2003) [hep-th/0305036];
111. Grumiller, D., Kummer, W.: "How to approach quantum gravity: Background independence in 1+1 dimensions," in What comes beyond the Standard Model? Symmetries beyond the standard model, Borstnik, N.M., Nielsen, H.B., Froggatt, C.D., Lukman, D. (eds.): vol. 4 of Bled Workshops in Physics, pp. 184-196, EURESCO. Portoroz, Slovenia, July (2003) [gr-qc/0310068.] based upon two talks;
112. Grumiller, D.: Deformations of the Schwarzschild black hole [gr-qc/0311011] Invited talk at MG X;
113. Bergamin, L., Grumiller, D., Kummer, W., Vassilevich, D.V.: Classical and quantum integrability of 2D dilaton gravities in Euclidean space [hep-th/0412007]
114. Bergamin, L., Grumiller, D., Kummer, W.: Quantization of 2d dilaton supergravity with matter. JHEP 05, 060 (2004) [hep-th/0404004]
115. Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems. Princeton University Press, 41 William Street, Princeton, New Jersey 08540, USA (1992)
116. Toms, D.J.: The functional measure for quantum field theory in curved space-time. Phys. Rev. D 35, 3796 (1987);
117. Fujikawa, K., Lindstrom, U., Nielsen, N.K., Rocek, M., van Nieuwenhuizen, P.: The regularized BRST coordinate invariant measure. Phys. Rev. D 37, 391 (1988)