Abstract
The interior of both Schwarzschild and Kantowski-Sachs black holes is studied via a non-canonical noncommutative extension of the Wheeler-DeWitt equation in the interesting work (Bastos et al. in Phys. Rev. D 84:024005, 2011) by neglecting the cubic and quartic terms arising the Hamiltonian. Here, we consider the problem when these terms are present and provide a more realistic analytical solution to the problem.
References
Agboola, D., Zhang, Y.: J. Math. Phys. 53, 042101 (2012)
Bertolami, O., Rosa, J.G., Aragão, C., Castorina, P., Zappalá, D.: Phys. Rev. D 72, 025010 (2005)
Bertolami, O., Zarro, C.: Phys. Lett. B 673, 83 (2009)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: J. Math. Phys. 49, 072101 (2008a)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Phys. Rev. D 78, 023516 (2008b)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Int. J. Mod. Phys. A 24, 2741 (2009a)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Phys. Rev. D 80, 124038 (2009b)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Phys. Rev. D 82, 041502 (2010)
Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Phys. Rev. D 84, 024005 (2011)
Connes, A., Douglas, M.R., Schwarz, A.: J. High Energy Phys. 9802, 003 (1998)
Dong, S.H.: Int. J. Theor. Phys. 40, 569 (2001)
Dong, S.H.: Wave Equations in Higher Dimensions. Springer, Dordrecht (2011)
Hassanabadi, H., Rajabi, A.: Few-Body Syst. 41, 201 (2007)
Hassanabadi, H., Yazarloo, B.H., Zarrinkamar, S., Rajabi, A.A.: Phys. Rev. C 84, 064003 (2011)
Hassanabadi, S., Rajabi, A.A., Zarrinkamar, S.: Mod. Phys. Lett. A 27, 1250057 (2012)
Kantowski, R., Sachs, R.K.: J. Math. Phys. 7, 443 (1966)
Konishi, K., Paffuti, G., Provero, P.: Phys. Lett. B 234, 276 (1990)
López-Dominguez, J.C., Obregón, O., Sabido, M., Ramirez, C.: Phys. Rev. D 74, 084024 (2006)
Maggiore, M.: Phys. Lett. B 304, 65 (1993)
Maggiore, M.: Phys. Rev. D 49, 5182 (1994)
Madore, J.: An Introduction to Noncommutative Differential Geometry and Its Physical Applications. Cambridge University Press, Cambridge (2002)
Nicolini, P.: Int. J. Mod. Phys. A 21, 1229 (2009)
Seiberg, N., Witten, E.: J. High Energy Phys. 9909, 032 (1999)
Szabo, R.: Phys. Rep. 378, 207 (2003)
Zhang, J.: Phys. Rev. Lett. 93, 043002 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zarrinkamar, S., Hassanabadi, H. & Rajabi, A.A. On the non-canonical noncommutative Wheeler-Dewitt equation for Schwarzschild and Kantowski-Sachs black holes. Astrophys Space Sci 344, 1–4 (2013). https://doi.org/10.1007/s10509-012-1329-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-012-1329-6