Vacuum energy, temperature corrections and heat kernel coefficients in $(D+1)$-dimensional spacetimes with nontrivial topology

Abstract

In this work we make use of the generalized zeta function technique to investigate the vacuum energy, temperature corrections and heat kernel coefficients associated with a scalar field under a quasiperiodic condition in a $(D+1)$-dimensional conical spacetime. In this scenario we find that the renormalized vacuum energy, as well as the temperature corrections, are both zero. The nonzero heat kernel coefficients are the ones related to the usual Euclidean divergence, and also to the nontrivial aspects of the quaisperiodically identified conical spacetime topology. An interesting result that arises in this configuration is that for some values of the quasiperiodic parameter, the heat kernel coefficient associated with the nontrivial topology vanishes. In addition, we also consider the scalar field in a $(D+1)$-dimensional spacetime formed by the combination of a conical and screw dislocation topological defects. In this case, we obtain a nonzero renormalized vacuum energy density and its corresponding temperature corrections. Again, the nonzero heat kernel coefficients found are the ones related to the Euclidean and nontrivial topology divergences. For $D=3$ we explicitly show, in the massless scalar field case, the limits of low and high temperatures for the free energy. In the latter, we show that the free energy presents a classical contribution.

18 pages, 3 Figures, version published in IJMPD

References in corpus (20)

• Measurement of the Casimir force between parallel metallic surfaces
• Volterra Distortions, Spinning Strings, and Cosmic Defects
• Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry
• Free and self-interacting scalar fields in the presence of conical singularities
• Vacuum currents induced by a magnetic flux around a cosmic string with finite core
• Results from electrostatic calibrations for measuring the Casimir force in the cylinder-plane geometry
• Induced vacuum bosonic current by magnetic flux in a higher dimensional compactified cosmic string spacetime
• Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
• Topological Casimir effect in compactified cosmic string spacetime
• Entanglement harvesting in cosmic string spacetime
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Basic zeta functions and some applications in physics
• Quantum vacuum fluctuation effects in a quasi-periodically identified conical spacetime
• Vacuum expectation value of the energy-momentum tensor in a higher dimensional compactified cosmic string spacetime
• Renormalized scalar propagator around a dispiration
• Ground state energy and topological mass in spacetimes with nontrivial topology
• Boundary effects on classical liquid density fluctuations
• Casimir effect, loop corrections and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions
• Semiclassical backreaction around a nearly spinning cosmic string
• Thermal Casimir effect in the Einstein Universe with a spherical boundary