  We analyse a quantum observer who falls geodesically towards the Cauchy
horizon of a $(1+1)$-dimensional eternal black hole spacetime with the global
structure of the non-extremal Reissner-Nordstr\"om solution. The observer
interacts with a massless scalar field, using an Unruh-DeWitt detector coupled
linearly to the proper time derivative of the field, and by measuring the local
energy density of the field. Taking the field to be initially prepared in the
Hartle-Hawking-Israel (HHI) state or the Unruh state, we find that both the
detector's transition rate and the local energy density generically diverge on
approaching the Cauchy horizon, respectively proportionally to the inverse and
the inverse square of the proper time to the horizon, and in the Unruh state
the divergences on approaching one of the branches of the Cauchy horizon are
independent of the surface gravities. When the outer and inner horizons have
equal surface gravities, the divergences disappear altogether in the HHI state
and for one of the Cauchy horizon branches in the Unruh state. We conjecture,
on grounds of comparison with the Rindler state in $1+1$ and $3+1$ Minkowski
spacetimes, that similar properties hold in $3+1$ dimensions for a detector
coupled linearly to the quantum field, but with a logarithmic rather than
inverse power-law divergence.
