New method for probing Kerr space-time based on imaging observation of in-falling gas blob

We propose a new observational method to probe the black hole space-time described by Einstein's theory.We consider a gas blob with an arc shape falling from the marginally stable orbit onto a black hole, carrying a finite amount of angular momentum. Previously, we proposed measuring the black hole spin from the flux variation data of the in-falling blob, assuming the Kerr space-time. We demonstrate here that we can independently measure the black hole spin solely by using the imaging data of the in-falling blob. We then introduce a Kerr-like hole (with one additional parameter which describes a stronger or weaker frame-dragging effect than that of the Kerr hole) and apply the two different methods of spin measurement: one based on the flux variation data and the other based on the imaging data. We obtain different spin values by the different methods for the Kerr-like hole. This is because these methods are sensitive to different components of the metric. We can in this way probe the black hole space-time through the comparison of the estimated spin values; that is, if the black hole space-time is described by the Kerr metric, all of them should coincide.