  We analyse the Hawking(-Unruh) effect for a massive Dirac spinor on the Z_2
quotient of Kruskal spacetime known as the RP^3 geon. There are two distinct
Hartle-Hawking-like vacua, depending on the choice of the spin structure, and
suitable measurements in the static region (which on its own has only one spin
structure) distinguish these two vacua. However, both vacua appear thermal in
the usual Hawking temperature to certain types of restricted operators,
including operators with support in the asymptotic future (or past). Similar
results hold in a family of topologically analogous flat spacetimes, where we
show the two vacua to be distinguished also by the shear stresses in the
zero-mass limit. As a by-product, we display the explicit Bogolubov
transformation between the Rindler-basis and the Minkowski-basis for massive
Dirac fermions in four-dimensional Minkowski spacetime.
