Fermionic Casimir densities for a uniformly accelerating mirror in the Fulling-Rindler vacuum

We investigate the local characteristics of the Fulling-Rindler vacuum for a massive Dirac field induced by a planar boundary moving with constant proper acceleration in ( D + 1 )-dimensional flat spacetime. On the boundary, the field operator obeys the bag boundary condition. The boundary divides the right Rindler wedge into two separate regions, called right-left (RL) and right-right (RR) regions. In both these regions, the fermion condensate and the vacuum expectation value (VEV) of the energy-momentum tensor are decomposed into two contributions. The first one presents the VEVs in the Fulling-Rindler vacuum when the boundary is absent and the second one is the boundary-induced contribution. For points away from the boundary, the renormalization is reduced to the one for the boundary-free geometry. The total VEVs are dominated by the boundary-free parts near the Rindler horizon and by the boundary-induced parts in the region near the boundary. For a massive field the boundary-free contributions in the fermion condensate and the vacuum energy density and effective pressures are negative everywhere. The boundary-induced contributions in the fermion condensate and the energy density are positive in the RL region and negative in the RR region. For a massless field the fermion condensate vanishes in spatial dimensions D ≥ 2 , while the VEV of the energy-momentum tensor is different from zero. This behavior contrasts with that of the VEVs in the Minkowski vacuum for the geometry of a boundary at rest relative to an inertial observer. In the latter case, the fermion condensate for a massless field is nonzero, while the VEV of the energy-momentum tensor becomes zero. The obtained results are used to investigate the VEV of the fermionic energy-momentum tensor in weak gravitational fields and background geometries that are conformally related to Rindler spacetime.