Polarization of the Fulling-Rindler vacuum by a uniformly accelerated mirror

Positive-frequency Wightman function and vacuum expectation values of the energy–momentum tensor are computed for a massive scalar field with general curvature coupling parameter, satisfying the Robin boundary condition on a uniformly accelerated infinite plate. Both the regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are investigated. For the case (ii) the electromagnetic field is considered as well. The mode summation method is used in combination with a variant of the generalized Abel–Plana formula. This allows us to present the expectation values in the form of a sum of the purely Rindler and boundary parts. Near the plate surface, the vacuum energy–momentum tensor is dominated by the boundary term. At large distances from the plate and near the Rindler horizon, the main contribution comes from the purely Rindler part. In the RL region, the vacuum energy density of the electromagnetic field is negative near the horizon and is positive near the plate.

[1]  A. Romeo,et al.  Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces , 2001, hep-th/0101155.

[2]  A. Saharian.  Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries , 2000, hep-th/0012185.

[3]  Jr.,et al.  Thermal fluctuations of a quantized massive scalar field in a Rindler background , 2000, gr-qc/0011038.

[4]  S. Solodukhin.  Boundary conditions and the entropy bound , 2000, gr-qc/0009103.

[5]  K. Milton.  Dimensional and Dynamical Aspects of the Casimir Effect: Understanding the Reality and Significance of Vacuum Energy , 2000, hep-th/0009173.

[6]  A. Romeo,et al.  Casimir effect for scalar fields under Robin boundary conditions on plates , 2000, hep-th/0007242.

[7]  A. Pomarol,et al.  Bulk fields and supersymmetry in a slice of AdS , 2000, hep-ph/0003129.

[8]  V. Mostepanenko,et al.  The Casimir Effect and Its Applications , 1997 .

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

[10]  K. Milton.  Vector Casimir effect for a D-dimensional sphere , 1996, hep-th/9611078.

[11]  A. Kamenshchik,et al.  Mixed boundary conditions in Euclidean quantum gravity , 1995, gr-qc/9506092.

[12]  L. Chimento,et al.  Exact Solutions of Quantum Massive Spin-1 Field Equations and Their Application to the Hawking-Unruh Effect , 1994 .

[13]  Milton,et al.  Scalar Casimir effect for a D-dimensional sphere. , 1994, Physical review. D, Particles and fields.

[14]  Torres,et al.  Dirac vacuum: Acceleration and external-field effects. , 1991, Physical review. D, Particles and fields.

[15]  J. Dowling.  The Mathematics of the Casimir Effect , 1989 .

[16]  I. Moss.  Boundary terms in the heat kernel expansion , 1989 .

[17]  Ooguri.  Spectrum of Hawking radiation and the Huygens principle. , 1986, Physical review. D, Particles and fields.

[18]  B. Müller,et al.  The Casimir effect , 1986 .

[19]  S. Takagi.  Vacuum Noise and Stress Induced by Uniform Acceleration Hawking-Unruh Effect in Rindler Manifold of Arbitrary Dimension , 1986 .

[20]  S. Takagi.  On the Response of a Rindler-Particle Detector , 1985 .

[21]  N. D. Birrell,et al.  Quantum fields in curved space , 2007 .

[22]  Stephen Wolfram,et al.  Properties of the vacuum. 2. Electrodynamic , 1983 .

[23]  Stephen Wolfram,et al.  Properties of the vacuum. I. mechanical and thermodynamic , 1983 .

[24]  D. Deutsch,et al.  On the vacuum stress induced by uniform acceleration or supporting the ether , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  D. Raine,et al.  Quantum field theory on incomplete manifolds , 1976 .

[26]  W. Unruh.  Notes on black-hole evaporation , 1976 .

[27]  P. Davies.  Scalar production in Schwarzschild and Rindler metrics , 1975 .

[28]  S. Fulling,et al.  Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time , 1973 .

[29]  K. S. Kölbig,et al.  Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints , 1972 .

[30]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[31]  C. Hill.  One Loop Operator Matrix Elements in the Unruh Vacuum , 1986 .

[32]  Mark T. Mueller,et al.  Covariant functional Schrödinger formalism and application to the Hawking effect , 1985 .