  The geodesics prescription in holographic approach in Lorentzian signature is
valid only for geodesics which connect spacelike-separated points at the
boundary, since there are no timelike geodesics which reach the boundary. There
is also no straightforward analytic Euclidean continuation for a general
background, such as e. g. moving particle in AdS. We propose an improved
geodesic image method for two-point Lorentzian correlators which is valid for
arbitrary time intervals in case of the bulk spacetime deformed by point
particles. We illustrate that our prescription is consistent with the case when
the analytic continuation exists and with the quasigeodesics prescription used
in previous work. We also discuss some other applications of the improved image
method, such as holographic entanglement entropy and multiple particles in
AdS3.
