Skip to Main Content

Access Provided by Xinjiang University

Physical Review D

Access by Xinjiang University

Electromagnetic Casimir piston in higher-dimensional spacetimes

Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500, Semenyih, Selangor Darul Ehsan, Malysia

^*LeePeng.Teo@nottingham.edu.my

Phys. Rev. D 83, 105020 – Published 19 May, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.105020

Abstract

We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form $M \times N$ , where $M$ is the four-dimensional Minkowski spacetime and $N$ is an $n$ -dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $N$ , the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the ( $4 + n$ )-dimensional Minkowski spacetime. However, if the size of $N$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1 + h / 2$ times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where $h$ is the first Betti number of $N$ . In the limit the manifold $N$ vanishes, one does not obtain the Casimir force in the four-dimensional Minkowski spacetime if $h$ is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.

Article Text

References (70)

H. B. G. Casimir, Proc. K. Ned. Akad. Wet. B51, 793 (1948).
M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford, 2009).
L. Perivolaropoulos, Phys. Rev. D 77, 107301 (2008).
E. Elizalde, Phys. Lett. B 516, 143 (2001).
C. L. Gardner, Phys. Lett. B 524, 21 (2002).
K. A. Milton, Gravitation Cosmol. 9, 66 (2003).
M. R. Setare, Eur. Phys. J. C 38, 373 (2004).
G. Mahajan, S. Sarkar, and T. Padmanabhan, Phys. Lett. B 641, 6 (2006).
M. Doran and J. Jaeckel, J. Cosmol. Astropart. Phys. 08 (2006) 010.
F. Pascoal, L. F. A. Oliveira, F. S. S. Rosa, and C. Farina, Braz. J. Phys. 38, 581 (2008).
H. Davoudiasl and E. Ponton, J. High Energy Phys. 10 (2010) 102.
F. S. Accetta, Phys. Rev. D 34, 1798 (1986).
W. D. Goldberger and I. Z. Rothstein, Phys. Lett. B 491, 339 (2000).
S. Nam, J. High Energy Phys. 10 (2000) 044.
W. H. Huang, J. High Energy Phys. 11 (2000) 041.
E. Ponton and E. Poppitz, J. High Energy Phys. 06 (2001) 019.
R. Hofmann, P. Kanti, and M. Pospelov, Phys. Rev. D 63, 124020 (2001).
W. H. Huang, Phys. Lett. B 497, 317 (2001).
N. Ahmed and I. G. Moss, Nucl. Phys. B 833, 133 (2010).
K. Poppenhaeger, S. Hossenfelder, S. Hofmann, and M. Bleicher, Phys. Lett. B 582, 1 (2004).
M. Frank, I. Turan, and L. Ziegler, Phys. Rev. D 76, 015008 (2007).
R. Linares, H. A. Morales-Técotl and O. Pedraza, Phys. Rev. D 77, 066012 (2008).
M. Frank, N. Saad, and I. Turan, Phys. Rev. D 78, 055014 (2008).
A. A. Saharian, Phys. Rev. D 73, 064019 (2006).
A. A. Saharian, Phys. Rev. D 73, 044012 (2006).
H. B. Cheng, Phys. Lett. B 668, 72 (2008).
A. Edery and V. N. Marachevsky, J. High Energy Phys. 12 (2008) 035.
K. Kirsten and S. A. Fulling, Phys. Rev. D 79, 065019 (2009).
E. Elizalde, S. D. Odintsov, and A. A. Saharian, Phys. Rev. D 79, 065023 (2009).
L. P. Teo, Phys. Lett. B 672, 190 (2009).
L. P. Teo, Nucl. Phys. B 819, 431 (2009).
L. P. Teo, J. High Energy Phys. 06 (2009) 076.
A. Flachi and T. Tanaka, Phys. Rev. D 80, 124022 (2009).
S. Bellucci and A. A. Saharian, Phys. Rev. D 80, 105003 (2009).
S. Bellucci and A. A. Saharian, Phys. Rev. D 79, 085019 (2009).
L. P. Teo, J. High Energy Phys. 11 (2009) 095.
M. Rypestol and I. Brevik, New J. Phys. 12, 013022 (2010).
M. Rypestol and I. Brevik, Phys. Scr. 82, 035101 (2010).
A. A. Saharian and M. R. Setare, Classical Quantum Gravity 27, 225009 (2010).
L. P. Teo, J. High Energy Phys. 10 (2010) 019.
R. M. Cavalcanti, Phys. Rev. D 69, 065015 (2004).
M. P. Hertzberg, R. L. Jaffe, M. Kardar, and A. Scardicchio, Phys. Rev. Lett. 95, 250402 (2005).
M. P. Hertzberg, R. L. Jaffe, M. Kardar, A. Scardicchio, Phys. Rev. D 76, 045016 (2007).
V. N. Marachevsky, Phys. Rev. D 75, 085019 (2007).
A. Edery, Phys. Rev. D 75, 105012 (2007).
A. Edery and I. Macdonald, J. High Energy Phys. 09 (2007) 005.
A. Edery and V. N. Marachevsky, Phys. Rev. D 78, 025021 (2008).
S. C. Lim and L. P. Teo, Eur. Phys. J. C 60, 323 (2009).
M. Schaden, Phys. Rev. A 79, 052105 (2009).
M. Schaden, J. Phys. Conf. Ser. 161, 012021 (2009).
E. Álvarez, F. D. Mazzitelli, A. G. Monastra, and D. A. Wisniacki, Phys. Rev. A 82, 052504 (2010).
K. A. Milton, J. Wagner, and K. Kirsten, Phys. Rev. D 80, 125028 (2009).
A. Edery, N. Graham, and I. McDonald, Phys. Rev. D 79, 125018 (2009).
S. A. Fulling, L. Kaplan, K. Kirsten, Z. H. Liu, and K. A. Milton, J. Phys. A 42, 155402 (2009).
M. Schaden, Phys. Rev. Lett. 102, 060402 (2009).
G. Barton, Phys. Rev. D 73, 065018 (2006).
G. Fucci and K. Kirsten, J. High Energy Phys. 03 (2011) 016.
Jan Ambjørn and S. Wolfram, Ann. Phys. (N.Y.) 147, 1 (1983).
E. Alvarez and F. D. Mazzitelli, Phys. Rev. D 79, 045019 (2009).
F. Chen, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Phys. Rev. A 69, 022117 (2004).
R. S. Decca, D. López, E. Fischbach, G. L. Klimchitskaya, D. E. Krause, and V. M. Mostepanenko, Phys. Rev. D 75, 077101 (2007).
R. S. Decca, D. López, E. Fischbach, G. L. Klimchitskaya, D. E. Krause, and V. M. Mostepanenko, Eur. Phys. J. C 51, 963 (2007).
G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009).
M. A. Rubin and C. Ordonez, J. Math. Phys. Sci. 26, 65 (1985).
B. Felsager, Geometry, Particles, and Fields (Springer Verlag, New York, 1998).
F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups (Springer Verlag, New York, 1983).
R. Sundrum, arXiv:hep-th/0508134.
V. K. Patodi, J. Indian Math. Soc. 34, 269 (1970).
T. P. Branson and P. B. Gilkey, Commun. Partial Differ. Equ. 15, 245 (1990).
N. Blazic, N. Bokan, and P. B. Gilkey, Indian J. Pure Appl. Math. 23, 103 (1992).