# Oral Presentation

A principle of measuring the BH's mass and spin via detecting the strong gravitational lens effect of Kerr BH

Presenter: Hiromi Saida (Daido University)

According to the general relativity (GR), the black hole (BH) is characterized by three parameters: mass M, spin angular momentum J and electric charge Q (the uniqueness theorem of BH spacetime in GR).

In real cases, the charge is expected to be zero, Q=0.

Then, the "BH observation" can be understood as the measurement of (M,J) through a direct observation of GR phenomena, for example the strong gravitational lens effect (bending of light by BH).

I am studying how the two parameters (M,J) appear in a time series data (light curve) seen by single telescope observing the strong gravitational lens effect by Kerr BH.

The situation treated in my study consists of three parts as follows:

(1) If an emission of light with short duration (burst-like emission) occurs near a BH, we focus on two light rays:

One light ray propagates from the source to observer along the shortest path which does not wind around the BH ("direct ray" or "zero-winding ray").

Another ray propagates along the secondary short path which winds once around the BH ("secondary ray" or "1-winding ray").

(2) When the observer detects the 0-winding and 1-winding rays by single telescope, he/she can (in principle) readout following two quantities from the light curve seen by the telescope:

Time delay between the detection times of 0-winding and 1-winding rays, Dt.

Ratio of brightness of 1-winding ray to that of 0-winding ray, RB.

(3) These two parameters (Dt,RB) are determined by BH parameters (M,J) and also the position and velocity (x,v) of source at the emission.

I will report how these quantities (M,J,x,v) determine the two observable quantities (Dt,RB).

Using this relation between (M,J,x,v) and (Dt,RB), we can measure the values of (M,J) by detecting (Dt,RB) in the time series data obtained by a telescople.

Also, it will be found that the estimated values of (Dt,RB) seem to be detectable by the present telescope capability.