×

Virtual black holes and the \(S\)-matrix. (English) Zbl 1067.83526

Summary: A brief review on virtual black holes is presented, with special emphasis on phenomenologically relevant issues like their influence on scattering or on the specific heat of (real) black holes. Regarding theoretical topics, the results important for (the avoidance of) information loss are summarized.
After recalling Hawking’s Euclidean notion of virtual black holes and a Minkowskian notion which emerged in studies of 2D models, the importance of virtual black holes for scattering experiments is addressed. Among the key features is that virtual black holes tend to regularize divergences of quantum field theory and that a unitary \(S\)-matrix may be constructed. Also, the thermodynamical behavior of real evaporating black holes may be ameliorated by interactions with virtual black holes. Open experimental and theoretical challenges are mentioned briefly.

MSC:

83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory
83C80 Analogues of general relativity in lower dimensions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Casimir H. B. G., Kon. Ned. Akad. Wetensch. Proc. 51 pp 793–
[2] DOI: 10.1016/S0370-1573(01)00015-1 · Zbl 0972.81212 · doi:10.1016/S0370-1573(01)00015-1
[3] Schwinger J., Quantum Electrodynamics (1958)
[4] Schuler G. A., Phys. Lett. 376 pp 193– · doi:10.1016/0370-2693(96)00265-1
[5] DOI: 10.1038/nature01121 · doi:10.1038/nature01121
[6] DOI: 10.1007/978-94-011-5139-9 · doi:10.1007/978-94-011-5139-9
[7] Hawking S. W., Phys. Rev. 53 pp 3099–
[8] Grumiller D., Nucl. Phys. 580 pp 438– · Zbl 0992.83054 · doi:10.1016/S0550-3213(00)00231-5
[9] DOI: 10.1016/S0370-1573(02)00267-3 · Zbl 0998.83038 · doi:10.1016/S0370-1573(02)00267-3
[10] J. Wheeler, Relativity, Groups and Topology, eds. C. DeWitt and B. DeWitt (Gordon and Breach, 1964) p. 316.
[11] Hawking S. W., Nucl. Phys. 144 pp 349– · doi:10.1016/0550-3213(78)90375-9
[12] DOI: 10.1887/0750306068 · doi:10.1887/0750306068
[13] Wall C. T. C., J. London Math. Soc. 39 pp 141–
[14] DOI: 10.1063/1.522935 · doi:10.1063/1.522935
[15] Hawking S. W., Phys. Rev. 56 pp 6403–
[16] Prestidge T., Phys. Rev. 58 pp 124022–
[17] Garay L. J., Int. J. Mod. Phys. 14 pp 4079– · Zbl 0960.83014 · doi:10.1142/S0217751X99001913
[18] Benatti F., Phys. Rev. 64 pp 085015–
[19] DOI: 10.1006/aphy.1998.5896 · Zbl 0966.82010 · doi:10.1006/aphy.1998.5896
[20] Rajaraman R., Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (1982) · Zbl 0493.35074
[21] Schaller P., Mod. Phys. Lett. 9 pp 3129– · Zbl 1015.81574 · doi:10.1142/S0217732394002951
[22] DOI: 10.1006/aphy.2001.6259 · doi:10.1006/aphy.2001.6259
[23] DOI: 10.1063/1.530216 · Zbl 0783.53051 · doi:10.1063/1.530216
[24] Kummer W., Nucl. Phys. 544 pp 403– · Zbl 0953.83024 · doi:10.1016/S0550-3213(99)00047-4
[25] DOI: 10.1088/0264-9381/14/4/007 · Zbl 0871.53074 · doi:10.1088/0264-9381/14/4/007
[26] DOI: 10.1063/1.529836 · Zbl 0764.53052 · doi:10.1063/1.529836
[27] DOI: 10.1088/0264-9381/21/24/012 · Zbl 1060.83045 · doi:10.1088/0264-9381/21/24/012
[28] Grumiller D., European Phys. J. 30 pp 135– · Zbl 1099.83535 · doi:10.1140/epjc/s2003-01258-5
[29] DOI: 10.1088/0264-9381/19/5/311 · Zbl 1006.83031 · doi:10.1088/0264-9381/19/5/311
[30] Kuchař K. V., Phys. Rev. 50 pp 3961–
[31] Adams F. C., Int. J. Mod. Phys. 16 pp 2399– · doi:10.1142/S0217751X0100369X
[32] Kobakhidze A. B., Phys. Lett. 514 pp 131– · Zbl 01629112 · doi:10.1016/S0370-2693(01)00776-6
[33] ’t Hooft G., Int. J. Mod. Phys. 11 pp 4623– · Zbl 1044.81683 · doi:10.1142/S0217751X96002145
[34] D. Grumiller, Proceedings of International Workshop on Mathematical Theories and their Applications, ed. S. Moskaliuk (Timpani, Cernivtsi, Ukraine, 2004) pp. 59–96, hep-th/0305073.
[35] DOI: 10.1142/1321 · doi:10.1142/1321
[36] Balasin H., Phys. Lett. 287 pp 138– · doi:10.1016/0370-2693(92)91889-H
[37] Henneaux M., Quantization of Gauge Systems (1992) · Zbl 0838.53053
[38] Moretti V., Nucl. Phys. 647 pp 131– · Zbl 1001.81064 · doi:10.1016/S0550-3213(02)00940-9
[39] Wald R. M., Living Rev. Rel. 4 pp 6– · Zbl 1060.83041 · doi:10.12942/lrr-2001-6
[40] DOI: 10.1142/1301 · doi:10.1142/1301
[41] DOI: 10.1002/(SICI)1521-3889(199912)8:10<801::AID-ANDP801>3.0.CO;2-O · Zbl 0948.83045 · doi:10.1002/(SICI)1521-3889(199912)8:10<801::AID-ANDP801>3.0.CO;2-O
[42] Gegenberg J., Phys. Rev. 51 pp 1781–
[43] DOI: 10.4310/ATMP.2000.v4.n1.a1 · Zbl 0981.83028 · doi:10.4310/ATMP.2000.v4.n1.a1
[44] DOI: 10.1103/PhysRevLett.81.4293 · Zbl 0949.83037 · doi:10.1103/PhysRevLett.81.4293
[45] DOI: 10.1088/0264-9381/21/23/002 · Zbl 1067.83536 · doi:10.1088/0264-9381/21/23/002
[46] Cadoni M., Phys. Rev. 59 pp 081501–
[47] DOI: 10.1088/0264-9381/16/10/322 · Zbl 0935.83023 · doi:10.1088/0264-9381/16/10/322
[48] DOI: 10.1103/PhysRevLett.88.241301 · doi:10.1103/PhysRevLett.88.241301
[49] Schwarzschild K., Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1916 pp 189–
[50] Katanaev M. O., Nucl. Phys. 486 pp 353– · Zbl 0925.83050 · doi:10.1016/S0550-3213(96)00624-4
[51] DOI: 10.1007/BF01208266 · doi:10.1007/BF01208266
[52] DOI: 10.1016/S0370-1573(99)00083-6 · Zbl 1368.81009 · doi:10.1016/S0370-1573(99)00083-6
[53] Brown J. D., Phys. Rev. 50 pp 6394–
[54] Zaslavsky O. B., Phys. Lett. 375 pp 43– · Zbl 0997.81551 · doi:10.1016/0370-2693(96)00188-8
[55] Grumiller D., J. High Energy Phys. 07 pp 009–
[56] DOI: 10.1088/0264-9381/21/15/N02 · Zbl 1070.83023 · doi:10.1088/0264-9381/21/15/N02
[57] Bergamin L., J. High Energy Phys. 05 pp 060–
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.