| Contents |
| We consider an inverse problem of the recovering of a part of a Lorentzian manifold $(M, g)$ from passive measurements. Namely, let $\mu([0,1])$ be a time-like curve and $U$ is its neighbourhood. Let $V$ be a relatively compact region in $J^-(\mu(1)) \setminus I^-(\mu(0))$, where $J^-(p)$ is the causal past of $p$. We assume that, for any $q \in V$ we know the set of the light observations $U \cap L^+(q)$, where $L^+(q)$ is the future light cone from $q$. Note that this type of data corresponds to the observation of supernovas, quasars, etc in astronomy.
Assuming that $(M, g)$ is strongly hyperbolic, we prove that this data uniquely determine $V$ and the conformal class of $g|_V$. |
|