  Relativistic quantum metrology is the study of optimal measurement procedures
within systems that have both quantum and relativistic components. Here we use
Unruh-DeWitt detectors coupled to a massless scalar field as probes of thermal
parameters in different spacetimes via a relativistic quantum metrology
analysis. We consider both (2+1)-dimensional anti-de Sitter and BTZ black hole
spacetimes. We compute the Fisher information to identify characteristics of
the black hole spacetime and to compare it to a uniformly accelerating detector
in anti-de Sitter space. We find the dependence of the Fisher information on
temperature, detector energy gap, black hole mass, interaction time, and the
initial state of the detector. We identify strategies that maximize the Fisher
information and therefore the precision of estimation.
