Brown and Maclay [1] found the energy-momentum tensor for the Casimir effect of parallel plates in 1969. We find its curved spacetime version in a static background using the point splitting regularization method. Previous results in the literature are reinforced and some consequences discussed.
L P Teo JHEP 10 (2010) 019; P Wongjun, Eur. Phys. J. C 75 (2015) 6; J Lorenzen and D Martelli JHEP 07 (2015) 001; A Edery and V Marachevsky, JHEP 12 (2008) 035.
Aram A Saharian, Phys. Rev. D 69 (2004) 085005.
A A Saharian, Int. J. Mod. Phys. A 26, 22 (2011) 3833.
E Elizalde, S D Odintsov and A A Saharian, Phys. Rev. D 83 (2011) 105023; E Elizalde, S D Odintsov and A A Saharian, Phys. Rev. D 79 (2009) 065023.
G Bimonte, E Calloni, G Esposito, and L Rosa, Phys. Rev. D 74 (2006) 085011; Erratum ibid. D 75 (2007) 049904, Erratum ibid. D 75 (2007) 089901; Erratum ibid. D 77 (2008) 109903.
G Bimonte, G Esposito, and L Rosa, Phys. Rev. D 78 (2008) 024010.
G Bimonte, E Calloni, G Esposito and L Rosa, Phys. Rev. D 76 (2007) 024010.
G Esposito, G M Napolitano, L Rosa, Phys.Rev.D 77 (2008) 105011.
G M Napolitano, G Esposito, L Rosa, Phys.Rev.D 78 (2008) 107701.
C W Misner, K S Thorne, J H Wheeler, Gravitation, W. H. Freeman and company, 1973.
S M Christensent, Phys.Rev. D 14 (1976) 2490.
C Ray Wylie and L C Barrett, Advanced engineering mathematics, 6th Ed., McGraw-Hill Inc., 1995, page 181.
S Hassani, Mathematical Physics:A Modern Introduction to Its Foundations, Second Edition, Springer, 2013, see Equ.(20.23).
B Toshmatov , Z Stuchlik, B Ahmedov, Mod. Phys. Lett. A 32 (2017) 1775001.
Borzoo Nazari, Quasi-local stress-tensor formalism and the Casimir effect, Mod. Phys. Lett. A 37 (2022) 2250160. https://doi.org/10.1142/S0217732322501607
E Elizalde, S D Odintsov, A Romeo, A A Bytsenko and S Zerbini, Zeta Function Regularization Techniques with Applications (World Scientific Publishing, 1994), doi:10.1142/2065.
I S Gradshteyn, I M Ryzhik, Table of Integrals, Series and Products, 7th edition, Elsevier Inc., 2007.
Nazari,B . (2025). Vacuum stress between conducting plates: the curved spacetime version. Iranian Journal of Physics Research, 25(3), 105-114. doi: 10.47176/ijpr.25.3.12050
MLA
Nazari,B . "Vacuum stress between conducting plates: the curved spacetime version", Iranian Journal of Physics Research, 25, 3, 2025, 105-114. doi: 10.47176/ijpr.25.3.12050
HARVARD
Nazari B. (2025). 'Vacuum stress between conducting plates: the curved spacetime version', Iranian Journal of Physics Research, 25(3), pp. 105-114. doi: 10.47176/ijpr.25.3.12050
CHICAGO
B Nazari, "Vacuum stress between conducting plates: the curved spacetime version," Iranian Journal of Physics Research, 25 3 (2025): 105-114, doi: 10.47176/ijpr.25.3.12050
VANCOUVER
Nazari B. Vacuum stress between conducting plates: the curved spacetime version. Iranian Journal of Physics Research. 2025;25(3):105-114 (In Persian). doi: 10.47176/ijpr.25.3.12050