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arXiv:2511.04547

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

A. A. Saharian, L. Sh. Grigoryan, V. Kh. Kotanjyan

hep-thgr-qcquant-phSubmitted Nov 6, 2025• Announced Nov 7, 2025• Revised Apr 21, 2026 (v2)
v1 · Nov 6, 2025v2 · Apr 21, 2026
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Abstract

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 RL and 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 $D\geq 2$, 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.

Journal reference
Phys. Rev. D 113 (2026) 085014
DOI
10.1103/r3hf-lcl8
Comments
31 pages, 4 figures, Section added on the Casimir densities in gravitational fields

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We explore entanglement harvesting using two Unruh-DeWitt (UDW) detectors linearly coupled to the scalar density of a massless spin-1/21/21/2 field in 1+11+11+1 Schwarzschild spacetime. We consider different vacua, including the Boulware, Hartle-Hawking-Israel (HHI), and Unruh vacua, and investigate various configurations of detector trajectories. We find that the transition rate of the static UDW detector exhibits the expected Planckian behavior in the HHI state, while the Unruh state leads to the Helmholtz free energy density of a fermionic thermal bath. We demonstrate that the near-horizon entanglement properties for static detectors in the HHI state have similar behavior to those in Minkowski vacua for uniformly accelerated detectors in Rindler spacetime. We further consider a different interaction Hamiltonian which breaks local Lorentz symmetry and find that the transition rate of the static detector still exhibits Planckian behavior in the HHI state, while in the Unruh state, it leads to the Helmholtz free energy density of a bosonic or fermionic thermal bath corresponding to the static or conformal 2-bein in interaction, respectively. We observe that the anti-Hawking effect enhances the entanglement between the two detectors while the gravitational redshift and Hawking radiation decrease it. In particular, due to the presence of the anti-Hawking effect, the mutual information and concurrence near the event horizon can be non-zero even for static detectors with static 2-bein, which is in contrast with the case of the scalar field. Conclusions are discussed.
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