Finite-temperature Casimir effect in Randall-Sundrum models
Abstract
The finite-temperature Casimir effect for a scalar field in the
bulk region of two Randall–Sundrum models, RSI and RSII, is studied.
We calculate the Casimir energy and the Casimir force for two parallel
plates with separation a on the visible brane in the RSI model. Hightemperature
and low-temperature cases are covered. Attraction versus repulsion
of the temperature correction to the force is discussed in the special cases
of Dirichlet–Dirichlet, Neumann–Neumann and Dirichlet–Neumann boundary
conditions at low temperature. The Abel–Plana summation formula is used, as
this is found to be the most convenient. Some comments are made on the related
contemporary literature.