Exact solutions of the Wheeler–DeWitt equation with ordering term in a dark energy scenario

Muniz, C. R.; Christiansen, H. R.; Cunha, M. S.; Vieira, H. S.

doi:10.1016/j.dark.2020.100547

Cited by 4 publications

(1 citation statement)

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“…These functions are related when imposing an equation of state among radial pressure and energy density p r = ρ. For = 3 one meets the conserved Casimir stress energy tensor (contributing only at the Planck scale); for = 1 the Ellis-Bronnikov wormhole (of sub-planckian size), = −1 is for ordinary vacuum and < −1 for phantom energy (see e.g., [24]).…”

Section: Introductionmentioning

confidence: 99%

Scalar Particles around a Rindler–Schwarzschild Wormhole

et al. 2022

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In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell.

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Section: Introductionmentioning

confidence: 99%