Vacuum expectation value of the energy-momentum tensor in a higher-dimensional compactified cosmic string spacetime

Abstract

The main objective of this paper is to analyze the vacuum expectation value (VEV) of the energy-momentum tensor (EMT) associated with a charged scalar quantum field in a high-dimensional cosmic string spacetime admitting the presence of a magnetic flux running along the string's core. In addition, we also assume that the coordinate along the string's axis is compactified to a circle and presents an extra magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase β. The calculation of the VEV of the EMT and field squared, are developed by using the positive-energy Wightman function. The latter is constructed by the mode sum of the complete set of normalized bosonic wave-functions. Due to the compactification, two distinct contributions take place. The first one corresponds to the VEV in a cosmic string spacetime without compactification considering the magnetic interaction. So, this term presents a contribution due to the non-trivial topology of the conical space, and an additional contribution due to the interaction between the scalar field with the magnetic flux. The latter is a periodic function of the magnetic flux with period equal to the quantum flux, Φ 0 = 2π/e, and corresponds to a Aharanov-Bhom type contribution. The second contribution is induced by the compactification itself and depends on the magnetic flux along the string's core. It is also an even function of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the VEVs of the energy-momentum tensor and field squared are provided for specific limiting cases of the physical parameter of the model.

Boundary effects on classical liquid density fluctuations

“…Moreover, the sum in n can be worked out by using the summation formula (25) from Ref. [25]. Subsequently, the integral in s can be solved which provides the closed and exact form for the two-point function, i.e., G(w, w ) = qu e iqβ∆ϕ 8π 2 ρ 0 rr…”

“…Note that the new sum in n in the two-point function, (16), is restricted to the interval [23,25,26]…”

Quantum vacuum fluctuation effects in a quasi-periodically identified conical spacetime

“…The procedure to perform the integrals and sum above requires that we first make a Wick rotation ∆τ = i∆t in (10) and, then, use the identities ( 19) and ( 21) of Ref. [31]. This allows us to evaluate the integrals in ν and η to obtain…”

“…However, theoretically, many works have been done considering the Casimir effect in spacetime with nontrivial topology, along with boundary conditions [2][3][4]18]. In this context, other components of the energy-momentum tensor have also been considered [5,6,[26][27][28][29][30][31][32].…”

Induced fermionic vacuum polarization in a de Sitter spacetime with a compactified cosmic string

“…The VEV of the induced fermionic current and the energy-momentum tensor considering a compactified cosmic string spacetime in the presence of a magnetic flux running through the string was studied in [37,38]. Moreover, for a charged scalar field, the VEVs of the induced bosonic current and energy-momentum tensor in a higher dimensional compactified cosmic string spacetime was considered in [39,40], respectively. For Schwarzschild spacetime equipped by a cosmic string, the vacuum polarization was investigated in [41,42].…”