CASIMIR ENERGY IN A CURVED BACKGROUND WITH A SPHERICAL BOUNDARY AND ARBITRARY RADIUS - AN EXACT SOLUTION VIA THE POINT SPLITTING METHOD

1994-05-15
BAYM, SS
OZCAN, M
We calculate the renormalized quantum vacuum energy-momentum tensor inside a spherical boundary, where the background geometry inside the boundary is represented by the closed static Friedmann metric. The remormalized energy density has two terms, one of which comes from the local curvature and the other one is due to the presence of the boundary. The renormalized energy density has a nonintegrable divergence as the boundary is approached.
PHYSICAL REVIEW D

Suggestions

Gravitational energy in quadratic-curvature gravities
Deser, S; Tekin, Bayram (2002-09-02)
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space...
Autoparallel orbits in Kerr Brans-Dicke spacetimes
Cebeci, H; Dereli, T; Tucker, RW (2004-01-01)
The bounded orbital motion of a massive spinless test particle in the background of a Kerr Brans-Dicke geometry is analysed in terms of worldlines that are auto-parallels of different metric compatible spacetime connections. In one case the connection is that of Levi-Civita with zero-torsion. In the second case the connection has torsion determined by the gradient of the Brans-Dicke background scalar field. The calculations permit one in principle to discriminate between these possibilities.
Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces
Shikakhwa, M. S.; Chair, N. (IOP Publishing, 2017-01-01)
We construct the Hermitian Schrodinger Hamiltonian of spin-less particles and the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field, which are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved...
Casimir energy of the massless conformal scalar field on S-2 by the point-splitting method
Bayin, SS; Ozcan, M (1997-10-01)
We calculate the Casimir energy of the massless conformal scalar held on the surface (S-2) of a 3 dimensional Riemann sphere by using the point-splitting, mode sum and the zeta-function renormalization methods. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. This problem is interesting since the Casimir energy could be calculated analytically by various methods, thus allowing us to compare different regularization schemes. (C) 1997 American Institute of Phys...
Singular potentials and moving boundaries in 3D
Yuce, C (Elsevier BV, 2004-02-16)
In this Letter, the problem of a spinless particle under the time-dependent harmonic oscillator potential and a singular potential with a moving boundary is studied in the spherical coordinates. Some transformations are used to transform the moving boundary conditions to the fixed boundary conditions. An exact solution is constructed.
Citation Formats
S. BAYM and M. OZCAN, “CASIMIR ENERGY IN A CURVED BACKGROUND WITH A SPHERICAL BOUNDARY AND ARBITRARY RADIUS - AN EXACT SOLUTION VIA THE POINT SPLITTING METHOD,” PHYSICAL REVIEW D, pp. 5313–5318, 1994, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64518.