Scalar particles around a Rindler-Schwarzschild wormhole

TL;DR

This paper explores quantum scalar fields around a Rindler-Schwarzschild wormhole, analyzing energy conditions, potential behavior, quantum tunneling, energy spectra, and Casimir energy to understand its quantum properties and stability.

Contribution

It introduces the Rindler-Schwarzschild wormhole spacetime, investigates energy condition violations, and computes quantum effects like tunneling spectra and Casimir energy.

Findings

Energy conditions are violated near the wormhole throat.

Scalar field potential is attractive and allows quantum tunneling.

Casimir energy and force are analytically derived.

Abstract

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 has to 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 nearby the wormhole throat and that 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. On imposing Dirichlet boundary conditions on a spherical shell nearby the throat we then 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 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.