Abstract
It is shown that exp(−2 Im(∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However, it is shown that this gives half the correct temperature for black holes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S W Hawking, Commun. Math. Phys. 43, 199 (1975), Erratum, Commun. Math. Phys. 46, 206 (1976)
J B Hartle and S W Hawking, Phys. Rev. D13, 2188 (1976)
S B Giddings, The black hole information paradox, arXiv:hep-th/9508151
W Israel, Nuovo Cimento B44S10, 1 (1966), Erratum, Nuovo Cimento B48, 463 (1967) NUCIA,B44,1.1966
P Kraus and F Wilczek, Nucl. Phys. B433, 403 (1995), arXiv:gr-qc/9408003
M K Parikh and F Wilczek, Phys. Rev. Lett. 85, 5042 (2000), arXiv:hep-th/9907001
E T Akhmedov, V Akhmedova, T Pilling and D Singleton, arXiv:hep-th/0605137.
S Q Wu and Q Q Jiang, arXiv:hep-th/0603082
Y P Hu, J Y Zhang and Z Zhao, arXiv:gr-qc/0601018
M Arzano, Phys. Lett. B634, 536 (2006), arXiv:gr-qc/0512071
I Radinschi, arXiv:gr-qc/0511142
M Nadalini, L Vanzo and S Zerbini, J. Phys. A39, 6601 (2006), arXiv:hep-th/0511250
A J M Medved and E C Vagenas, Mod. Phys. Lett. A20, 2449 (2005), arXiv:grqc/0504113
R Kerner and R B Mann, Phys. Rev. D73, 104010 (2006), arXiv:gr-qc/0603019
K Melnikov and M Weinstein, Int. J. Mod. Phys. D13, 1595 (2004), arXiv:hepth/0205223
J G Zhang, Y P Hu and Z Zhao, arXiv:hep-th/0512121
M B Einhorn, arXiv:hep-th/0510148
B Greene, M Parikh and J P van der Schaar, arXiv:hep-th/0512243
V D Gladush, J. Math. Phys. 42, 2590 (2001), arXiv:gr-qc/0001073
V A Rubakov, Classical theory of gauge fields (Princeton University Press, USA, 2002)
E Poisson, A relativist’s toolkit (Cambridge University Press, UK, 2004)
M Heusler, C Kiefer and N Straumann, Phys. Rev. D42, 4254 (1990), Erratum, Phys. Rev. D44, 1342 (1991)
K Srinivasan and T Padmanabhan, Phys. Rev. D60, 024007 (1999), arXiv:gr-qc/9812028
Here outer horizon means the outer horizon of a multiple horizon black hole and not the horizon of the outer manifold of the shell. In [2] since there are only test shells, there is just one manifold
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chowdhury, B.D. Problems with tunneling of thin shells from black holes. Pramana - J Phys 70, 3–26 (2008). https://doi.org/10.1007/s12043-008-0001-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0001-8