Energy-momentum tensor for a Casimir apparatus in a weak gravitational field

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane-parallel conducting plates is derived. We use Fermi coordinates and work to first order in the constant acceleration parameter. A perturbative expansion, to this order, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point-splitting procedure. In correspondence to the Green functions satisfying mixed and gauge-invariant boundary conditions, and Ward identities, the energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts, while a new simple formula for the trace anomaly is obtained to first order in the constant acceleration. A more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction.

[1]  A. Saharian,et al.  WIGHTMAN FUNCTION AND CASIMIR DENSITIES FOR ROBIN PLATES IN THE FULLING–RINDLER VACUUM , 2005, hep-th/0504189.

[2]  F. Sorge.  Casimir effect in a weak gravitational field , 2005 .

[3]  P. Davies.  Quantum vacuum friction , 2005 .

[4]  L. Milano,et al.  On the photon Green functions in curved spacetime , 2003, hep-th/0310049.

[5]  A. Saharian.  Energy-momentum tensor for a scalar field on manifolds with boundaries , 2003, hep-th/0308108.

[6]  Letter: Casimir Stress for Cylindrical Shell in de Sitter Space , 2002, hep-th/0203029.

[7]  R. Caldwell.  Gravitation of the Casimir Effect and the Cosmological Non-Constant , 2002, astro-ph/0209312.

[8]  M. Setare,et al.  Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background , 2002, gr-qc/0207081.

[9]  H. Weigel,et al.  Calculating vacuum energies in renormalizable quantum field theories:: A new approach to the Casimir problem , 2002, hep-th/0207120.

[10]  U. Mohideen,et al.  New developments in the Casimir effect , 2001, quant-ph/0106045.

[11]  G. Barton,et al.  Perturbative Casimir energies of dispersive spheres, cubes and cylinders , 2001 .

[12]  M. Setare,et al.  CASIMIR EFFECT FOR A SPHERICAL SHELL IN DE SITTER SPACE–TIME WITH SIGNATURE CHANGE , 2000, hep-th/0511077.

[13]  I. Avramidi,et al.  Gauge Theories on Manifolds with Boundary , 1997, hep-th/9710048.

[14]  A. Kamenshchik,et al.  Euclidean Quantum Gravity on Manifolds with Boundary , 1997 .

[15]  F. Antonsen,et al.  The Casimir Effect of Curved Space-time (formal developments) , 1996, hep-th/9608142.

[16]  Bayin,et al.  Casimir energy in a curved background with a spherical boundary and arbitrary radius: An exact solution via the point splitting method. , 1994, Physical review. D, Particles and fields.

[17]  Marzlin.  Fermi coordinates for weak gravitational fields. , 1994, Physical review. D, Particles and fields.

[18]  Bayin,et al.  Casimir energy in a curved background with a spherical boundary: An exactly solvable case. , 1993, Physical review. D, Particles and fields.

[19]  S. Bayin,et al.  Casimir effect in a 'half Einstein universe': an exactly solvable case in curved background and with a spherical boundary , 1993 .

[20]  Brown,et al.  Photon propagators and the definition and approximation of renormalized stress tensors in curved space-time. , 1986, Physical review. D, Particles and fields.

[21]  R. Endo.  Gauge Dependence of the Grabvitational Conformal Anomaly for the Electromagnetic Field , 1984 .

[22]  D. Deutsch,et al.  Boundary effects in quantum field theory , 1979 .

[23]  L. Parker,et al.  Feynman propagator in curved spacetime: A momentum-space representation , 1979 .

[24]  S. Christensen.  Regularization, renormalization, and covariant geodesic point separation , 1978 .

[25]  S. Christensen.  Vacuum Expectation Value of the Stress Tensor in an Arbitrary Curved Background: The Covariant Point Separation Method , 1976 .

[26]  B. Dewitt,et al.  Quantum field theory in curved spacetime , 1975 .

[27]  N. Kampen,et al.  ON THE MACROSCOPIC THEORY OF VAN DER WAALS FORCES , 1968 .

[28]  J. Synge,et al.  Relativity: The General Theory , 1960 .

[29]  J. Synge.  A Characteristic Function in Riemannian Space and its Application to the Solution of Geodesic Triangles , 1931 .

[30]  H. S. Ruse.  Taylor's theorem in the tensor calculus , 1931 .

[31]  L. Lorenz.  XXXVIII. On the identity of the vibrations of light with electrical currents , 1867 .