Abstract
The Klein-Gordon equation under the influence of the gravitational field produced by a topology such as the Som-Raychaudhuri spacetime and the Klein-Gordon oscillator in the presence of a uniform magnetic field as well as without magnetic field are investigated. Moreover, the Klein-Gordon equation with a cylindrically symmetric scalar potential in the background spacetime is also studied. By using the quasi-analytical ansatz approach, we obtain the energy eigenvalues and corresponding wave functions of these systems. They show that the energy levels of the considered physical systems depend explicitly on the angular deficit α and the vorticity parameter Ω which characterize the global structure of the metric in the Som-Raychaudhuri spacetime.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Vilenkin, Phys. Lett. B 133, 177 (1983).
A. Vilenkin, Phys. Rep. 121, 263 (1985).
T.W. Kibble, J. Phys. A 19, 1387 (1976).
B. Linet, Gen. Relativ. Gravit. 17, 1109 (1985).
W.A. Hiscock, Phys. Rev. D 31, 3288 (1985).
M. Barriola, A. Vilenki, Phys. Rev. Lett. 63, 341 (1989).
M. Cruz, N. Turok, P. Vielva, E. Martinez-Gonzalez, M. Hobson, Science 318, 1612 (2007).
G. de A. Marques, V.B. Bezerra, Phys. Rev. D 66, 105011 (2002).
V.B. Bezerra, Braz. J. Phys. 36, 1B (2006).
G. de A. Marques, V.B. Bezerra, Class. Quantum Grav. 19, 985 (2002).
C. Furtado, F. Moraes, V.B. Bezerra, Phys. Lett. A 289, 160 (2001).
J.L. A. Coelho, R.L.P.G. Amaral, J. Phys. A: Math. Gen. 35, 5255 (2002).
C. Furtado, F. Moraes, Phys. Lett. A 188, 394 (1994).
K. Bakke, J.R. Nascimento, C. Furtado, Phys. Rev. D 78, 064012 (2008).
K. Bakke, L.R. Ribeiro, C. Furtado, J.R. Nascimento, Phys. Rev. D 79, 024008 (2009).
C. Furtado, F. Moraes, Phys. Lett. A 195, 90 (1994).
G. de A. Marques, C. Furtado, V.B. Bezerra, F. Moraes, J. Phys. A: Math. Gen. 31, 5945 (2001).
E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012).
J. Carvalho, A.M. de M. Carvalho, C. Furtado, Eur. Phys. J. C 74, 2935 (2014).
L. Parker, Phys. Rev. Lett. 44, 1559 (1980).
L. Parker, L.O. Pimentel, Phys. Rev. D 25, 3180 (1982).
S. Moradi, E. Aboualizadeh, Gen. Relativ. Gravit. 42, 435 (2010).
K. Gödel, Rev. Mod. Phys. 21, 447 (1949).
E.K. Boyda, S. Ganguli, P. Hořava, U. Varadarajan, Phys. Rev. D 67, 106003 (2003).
M. Rebouças, J. Tiomno, Phys. Rev. D 28, 1251 (1983).
M.M. Som, A.K. Raychaudhuri, Proc. R. Soc. A 304, 81 (1968).
A. Boumali, N. Messai, Can. J. Phys. 92, 1 (2014).
D.H. Perkins, An Introduction to High Energy Physics (Cambridge University Press, Cambridge, 2000).
G.E. Andrews, R. Askey, A. Roy, Special Functions (Cambridge University Press, Cambridge, 1999).
N. Drukker, B. Fiol, J. Simón, JCAP 10, 012 (2004).
S. Yu. Slavyanov, W. Lay, Special Functions: A Unified Theory Based in Singularities (Oxford University Press, New York, 2000).
A.L. Cavalcanti de Oliveira, E.R. Bezerra de Mello, Class. Quantum Grav. 22, 1255 (2005).
M. Hamzavi, A.A. Rajabi, Ann. Phys. 334, 316 (2013).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, Z., Long, Zw., Long, Cy. et al. Relativistic quantum dynamics of a spinless particle in the Som-Raychaudhuri spacetime. Eur. Phys. J. Plus 130, 36 (2015). https://doi.org/10.1140/epjp/i2015-15036-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2015-15036-2