  We investigate the intrinsic uncertainty in the accuracy to which a static
spacetime can be measured from scattering experiments. In particular, we focus
on the Schwarzschild black hole and a spatially kinked metric that has some
mathematical resemblance to an expanding universe. Under selected conditions we
find that the scattering problem can be framed in terms of a lossy bosonic
channel, which allows us to identify shot-noise scaling as the ultimate
scaling-limit to the estimation of the spacetimes. Fock state probes with
particle counting measurements attain this ultimate scaling limit and the
scaling constants for each spacetime are computed and compared to the practical
strategies of coherent state probes with heterodyne and homodyne measurements.
A promising avenue to analyze the quantum-limit of the analogue spacetimes in
optical waveguides is suggested.
