Estimating black hole mass by weak measurements

We address the estimation of the black hole mass probed by two modes of a Dirac field described by relatively accelerated observers in the Schwarzschild spacetime. We present an analytical analysis of the quantum Fisher information and discuss how the optimal estimation of the black hole mass can be enhanced by weak measurements designed before and after the accelerating observer. Moreover, we propose a feasible measurement for the optimal estimation. It is shown that massive black holes forbid leakage of the information about their structure, leading to ambiguity about their structure. Our work generalizes the ability of weak measurements as an effective quantum technique to enhance relativistic quantum metrology in a gravitational scenario.