  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.
