Remarks on the determination of the Lorentzian metric by the lengths of geodesics or null-geodesics

Gregory Eskin

We consider a Lorentzian metric in $\mathbb{R}\times {\mathbb{R}}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,\eta )$ when $t=0$, then we can rec…