Quantum amplitudes in black-hole evaporation: spins 1 and 2. (English) Zbl 1097.83018
Spin 1 and spin 2 perturbations of a background describing the gravitational collapse to a black hole are investigated, and the corresponding quantum amplitudes are obtained.
Reviewer: Mohammad Khorrami (Tehran)
MSC:
| 83C57 | Black holes |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
References:
| [1] | Parikh, M. K.; Wilczek, F., Phys. Rev. Lett., 85, 5042 (2000) · Zbl 1369.83053 |
| [2] | Parikh, M., Gen. Relativ. Gravit., 36, 2419 (2004) · Zbl 1063.83013 |
| [3] | Commun. Math. Phys., 43, 199 (1975) |
| [4] | Hájíček, P.; Israel, W., Phys. Lett. A, 80, 9 (1980) |
| [5] | Bardeen, J., Phys. Rev. Lett., 46, 382 (1981) |
| [6] | Hawking, S. W., Commun. Math. Phys., 87, 395 (1982) · Zbl 0506.76138 |
| [7] | Hawking, S. W., (Brück, H. A.; Coyne, G. V.; Longair, M. S., Astrophysical Cosmology. Astrophysical Cosmology, Proceedings of the Study Week on Cosmology and Fundamental Physics, vol. 48 (1982), Pontificia Academiae Scientarium: Pontificia Academiae Scientarium Vatican City), 563 |
| [8] | Wald, R. M., (Christensen, S., Quantum Theory of Gravity (1984), Adam Hilger: Adam Hilger Bristol), 160 |
| [9] | A.N.St.J. Farley, Quantum Amplitudes in Black-Hole Evaporation, Cambridge Ph.D. dissertation, approved 2002 (unpublished).; A.N.St.J. Farley, Quantum Amplitudes in Black-Hole Evaporation, Cambridge Ph.D. dissertation, approved 2002 (unpublished). · Zbl 1097.83018 |
| [10] | S.W. Hawking, communication, GR17 Conference, Dublin, 18-24 July (2004).; S.W. Hawking, communication, GR17 Conference, Dublin, 18-24 July (2004). |
| [11] | Farley, A. N.St. J.; D’Eath, P. D., Phys Lett. B, 601, 184 (2004) · Zbl 1247.83082 |
| [12] | Shellard, E. P.S., (Gibbons, G. W.; Shellard, E. P.S.; Rankin, S. J., The Future of Theoretical Physics and Cosmology (2003), Cambridge University Press: Cambridge University Press Cambridge), 755 · Zbl 1176.83002 |
| [13] | Feynman, R. P.; Hibbs, A. R., Quantum Mechanics and Path Integrals (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0176.54902 |
| [14] | Garabedian, P. R., Partial Differential Equations (1964), Wiley: Wiley New York · Zbl 0124.30501 |
| [15] | D’Eath, P. D., Supersymmetric Quantum Cosmology (1996), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0889.53052 |
| [16] | Farley, A. N.St. J.; D’Eath, P. D., Phys Lett. B, 613, 181 (2005) · Zbl 1247.83083 |
| [17] | Reula, O., A Configuration Space for Quantum Gravity and Solutions to the Euclidean Einstein Equations in a Slab Region (1987), Max-Planck-Institut fur Astrophysik: Max-Planck-Institut fur Astrophysik MPA, pp. 275 |
| [18] | Commun. Pure Appl. Math., 46, 1131 (1993) |
| [19] | D’Eath, P. D.; Sornborger, A., Class. Quantum Grav., 15, 3435 (1998) · Zbl 0946.83021 |
| [20] | P.D. D’Eath, Numerical and analytic estimates for Einstein/scalar boundary-value problems, in progress.; P.D. D’Eath, Numerical and analytic estimates for Einstein/scalar boundary-value problems, in progress. |
| [21] | Das, A.; Fischler, M.; Roček, M., Phys.Lett. B, 69, 186 (1977) |
| [22] | Wess, J.; Bagger, J., Supersymmetry and Supergravity (1992), Princeton University Press: Princeton University Press Princeton |
| [23] | Hartle, J. B.; Hawking, S. W., Phys. Rev. D, 28, 2960 (1983) · Zbl 1370.83118 |
| [24] | Dirac, P. A.M., Lectures on Quantum Mechanics (1965), Academic Press: Academic Press New York · Zbl 0060.45102 |
| [25] | D’Eath, P. D., (Sánchez, N., Fundamental Problems in Classical, Quantum and String Gravity (1999), Observatoire de Paris), 166, Available from: |
| [26] | D’Eath, P. D., (Gibbons, G. W.; Shellard, E. P.S.; Rankin, S. J., The Future of Theoretical Physics and Cosmology (2003), Cambridge University Press: Cambridge University Press Cambridge), 693 · Zbl 1176.83002 |
| [27] | Faddeev, L. D., (Balian, R.; Zinn-Justin, J., Methods in Field Theory (1976), North-Holland: North-Holland Amsterdam) |
| [28] | Faddeev, L. D.; Slavnov, A. A., Gauge Fields: Introduction to Quantum Theory (1980), Benjamin/Cummings: Benjamin/Cummings Reading, Mass · Zbl 0486.53052 |
| [29] | Itzykson, C.; Zuber, J.-B., Quantum Field Theory (1980), McGraw-Hill: McGraw-Hill New York · Zbl 0453.05035 |
| [30] | D’Eath, P. D., Black Holes: Gravitational Interactions (1996), Oxford University Press: Oxford University Press Oxford · Zbl 0874.53057 |
| [31] | ’t Hooft, G., Phys. Lett. B, 198, 61 (1987) |
| [32] | Giddings, S., (Gibbons, G. W.; Shellard, E. P.S.; Rankin, S. J., The Future of Theoretical Physics and Cosmology (2003), Cambridge University Press: Cambridge University Press Cambridge), 278 · Zbl 1176.83002 |
| [33] | A.N.St.J. Farley, P.D. D’Eath, Quantum Amplitudes in Black-Hole Evaporation: I. Complex Approach, 2005, submitted for publication.; A.N.St.J. Farley, P.D. D’Eath, Quantum Amplitudes in Black-Hole Evaporation: I. Complex Approach, 2005, submitted for publication. |
| [34] | A.N.St.J. Farley, P.D. D’Eath, ‘Quantum Amplitudes in Black-Hole Evaporation: II. Spin-0 Amplitude, 2005, submitted for publication.; A.N.St.J. Farley, P.D. D’Eath, ‘Quantum Amplitudes in Black-Hole Evaporation: II. Spin-0 Amplitude, 2005, submitted for publication. |
| [35] | Farley, A. N.St. J.; D’Eath, P. D., Class. Quantum Grav., 22, 3001 (2005) · Zbl 1129.83325 |
| [36] | A.N.St.J. Farley, P.D. D’Eath, Spin-3/2 Amplitudes in Black-Hole Evaporation, in progress.; A.N.St.J. Farley, P.D. D’Eath, Spin-3/2 Amplitudes in Black-Hole Evaporation, in progress. |
| [37] | Mathews, J., J. Soc. Ind. Appl. Math., 10, 768 (1962) · Zbl 0114.21201 |
| [38] | Goldberg, J. N.; MacFarlane, A. J.; Newman, E. T.; Rohrlich, F.; Sudarshan, E. C.G., J. Math. Phys., 8, 2155 (1967) · Zbl 0155.57402 |
| [39] | Futterman, J. A.H.; Handler, F. A.; Matzner, R. A., Scattering from Black Holes (1988), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1187.85003 |
| [40] | Stephani, H., Exact Solutions to Einstein’s Field Equations (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0552.35062 |
| [41] | Vaidya, P. C., Proc. Indian Acad. Sci. A, 33, 264 (1951) · Zbl 0044.42202 |
| [42] | R. Penrose, W. Rindler, Spinors and Space-Time, vol. 1 Cambridge University Press, Cambridge (1984).; R. Penrose, W. Rindler, Spinors and Space-Time, vol. 1 Cambridge University Press, Cambridge (1984). · Zbl 0538.53024 |
| [43] | R. Penrose, W. Rindler, Spinors and Space-Time, vol. 2 Cambridge University Press, Cambridge (1986).; R. Penrose, W. Rindler, Spinors and Space-Time, vol. 2 Cambridge University Press, Cambridge (1986). · Zbl 0591.53002 |
| [44] | Eguchi, T.; Gilkey, P. B.; Hanson, A. J., Phys. Rep., 66, 214 (1980) |
| [45] | A.N.St.J. Farley, P.D. D’Eath, Bogoliubov Transformations in Black-Hole Evaporation, 2005, submitted for publication.; A.N.St.J. Farley, P.D. D’Eath, Bogoliubov Transformations in Black-Hole Evaporation, 2005, submitted for publication. · Zbl 1247.83083 |
| [46] | Ward, R. S.; Wells, R. O., Twistor Geometry and Field Theory (1990), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0729.53068 |
| [47] | Nakahara, M., Geometry, Topology and Physics (2003), Institute of Physics: Institute of Physics Bristol · Zbl 1090.53001 |
| [48] | Hawking, S. W.; Ellis, G. F.R., The large scale structure of space-time (1973), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0265.53054 |
| [49] | Misner, C. W.; Thorne, K. S.; Wheeler, J. A., Gravitation (1973), Freeman: Freeman San Francisco |
| [50] | Wheeler, J. A., (DeWitt, C.; DeWitt, B., Relativity, Groups and Topology (1964), Blackie and Son: Blackie and Son London), 317 |
| [51] | Wheeler, J. A., (DeWitt, C. M.; Wheeler, J. A., Battelle Rencontres (1968), Benjamin: Benjamin New York), 242 |
| [52] | D’Eath, P. D., Phys. Rev. D, 11, 1387 (1975) |
| [53] | Thorne, K. S.; Price, R. H.; Macdonald, D. A., Black holes. The membrane paradigm (1986), Yale University Press: Yale University Press New Haven, Ct. · Zbl 1374.83002 |
| [54] | Atiyah, M. F.; Hitchin, N. J.; Singer, I. M., Proc. R. Soc. Lond. A., 362, 425 (1978) · Zbl 0389.53011 |
| [55] | Newman, E. T.; Penrose, R., J. Math. Phys., 3, 566 (1962) |
| [56] | Teukolsky, S. A., Astrophys. J., 185, 635 (1973) |
| [57] | Chandrasekhar, S., The Mathematical Theory of Black Holes (1992), Oxford University Press: Oxford University Press Oxford · Zbl 0511.53076 |
| [58] | Geroch, R.; Held, A.; Penrose, R., J. Math. Phys., 14, 874 (1973) · Zbl 0875.53014 |
| [59] | Kinnersley, W., J. Math. Phys, 10, 1195 (1969) · Zbl 0182.30202 |
| [60] | Jackson, J. D., Classical Electrodynamics (1975), Wiley: Wiley New York · Zbl 0114.42903 |
| [61] | Chrzanowski, P. L., Phys. Rev D, 11, 2042 (1975) |
| [62] | Wald, R. M., Phys. Rev. Lett., 41, 203 (1978) |
| [63] | Regge, T.; Wheeler, J. A., Phys. Rev., 108, 1063 (1957) · Zbl 0079.41902 |
| [64] | Zerilli, F. J., Phys. Rev. D, 2, 2141 (1970) · Zbl 1227.83025 |
| [65] | Cunningham, C. T.; Price, R. H.; Moncrief, V., Astrophys. J., 230, 870 (1979) |
| [66] | Wheeler, J. A., Geometrodynamics (1962), Academic Press: Academic Press New York · Zbl 0124.22207 |
| [67] | Thorne, K. S.; Campolattaro, A., Astrophys. J., 149, 591 (1967) |
| [68] | Moncrief, V., Ann. Phys. (NY), 88, 323 (1974) |
| [69] | A.N.St.J. Farley, P.D. D’Eath, Vaidya Space-Time in Black-Hole Evaporation, Gen. Relativ. Gravit. (2006).; A.N.St.J. Farley, P.D. D’Eath, Vaidya Space-Time in Black-Hole Evaporation, Gen. Relativ. Gravit. (2006). · Zbl 1097.83019 |
| [70] | Zerilli, F. J., Phys. Rev. D, 9, 860 (1974) |
| [71] | Breitenlohner, P.; Freedman, D. Z., Phys. Lett. B, 115, 197 (1982) |
| [72] | Breitenlohner, P.; Freedman, D. Z., Ann. Phys. (NY), 144, 249 (1982) · Zbl 0606.53044 |
| [73] | Hawking, S. W., Phys. Lett. B, 126, 175 (1983) |
| [74] | Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1964), Dover: Dover New York · Zbl 0515.33001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
