Document Type : Original Article
Author
College of engineering, University of Tehran, Tehran
Abstract
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.
Keywords
Main Subjects
- L S Brown and G J Maclay, Phys. Rev. 184 (1969) 1272.
- S Hawking, Nature 248 (1974) https://doi.org/10.1038/248030a0
- L Parker, The Physical Review 183 (5) (1969);L Parker, The Physical Review, 3(2) (1972).
- N D Birrell, and P C W Davies, Quantum field theory in curved spacetime, Cambridge universsity press , 1982.
- B S DeWitt, Phys. Rep. 19 (1975) 295.
- K A Milton , Prachi Parashar, K V Shajesh, and Jef Wagner, J. Phys. A 40 (2007) 10935.
- S A Fulling, K A Milton, P Parashar, A Romeo, KV Shajesh, J Wagner Phys. Rev. D 76 (2007) 025004.
- K A Milton, K V Shajesh, S A Fulling, Prachi Parashar, Phys. Rev. D 89 (2014) 064027.
- K V Shajesh, Kimball A Milton, Prachi Parashar and Jeffrey A Wagner, J. Phys. A: Math. Theor. 41 (2008) 164058.
- E Calloni, L Di Fiore, G Esposito, L Milano and L Rosa, Phys. Lett. A 297 (2002) 328.
- M Nouri-zonoz, Borzoo Nazari, Phys. Rev. D 82 (2010) 044047.
- Borzoo Nazari, M Nouri-zonoz , Phys. Rev. D 85 (2012) 044060.
- Aram A Saharian, Phys. Rev. D 70, (2004) 064070.
- V B Bezerra, H F Mota, C R Muniz, Phys.Rev.D 89 (2014) 044015.
- F Sorge, Phys. Rev. D 90 (2014) 084050.
- C R Muniz, V B Bezerra, M S Cunha, Phys. Rev. D 88 (2013) 104035.
- C R Muniz, V B Bezerra, M.S. Cunha, Annals of Physics 359 (2015) 55.
- F Sorge, Class. Quantum. Grav. 22 (2005) 5109.
- F Sorge, Class. Quantum Grav. 36 (2019) 235006.
- A P C M Lima, G Alencar, C R Muniz and R R Landim, JCAP 07 (2019) 011.
- Massimo Blasone, Gaetano Lambiase, Luciano Petruzziello, Antonio Stabile, Eur. Phys. J. C 78 (2018) 976.
- Luca Buoninfante, Gaetano Lambiase, Luciano Petruzziello, Antonio Stabile, Eur. Phys. J. C 79 (2019) 41.
- G Lambiase, A Stabile and An Stabile, Phys. Rev.D 95 (2017) 084019.
- Borzoo Nazari, Eur. Phys. J. C 75 (2015) 501.
- Borzoo Nazari, Class. Quantum Grav. 37 (2020) 135014.
- 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.
)