Finite temperature energy–momentum tensor in compactified cosmic string spacetime

In this paper we analyze the expectation value of the field squared and the energy–momentum tensor associated with a massive charged scalar quantum field with a nonzero chemical potential propagating in a high-dimensional compactified cosmic string spacetime in thermal equilibrium at finite temperature T. Moreover, we assume that the charged quantum field interacts with a very thin magnetic flux running along the core of the idealized cosmic string, and with a magnetic flux enclosed by the compact dimension. These observables are expressed as the vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitations. Due to the compactification, the thermal corrections can be decomposed in a part induced by the cosmic string spacetime without compactification, plus a contribution induced by the compactification. This decompositions explicitly follows from the Abel–Plana formula used to proceed the summation over the discrete quantum number associated with the quasiperiodic condition imposed on the quantum field along the compact dimension. The expectations values of the field squared and the energy–momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Our main objectives in this paper concern in the investigation of the thermal corrections only. In this way we explicitly calculate the behavior of these observables in the limits of low and high temperature. We show that the temperature enhance the induced densities. In addition some graphs are also included in order to exhibit these behaviors.