How to measure a black hole’s mass, spin, and direction of spin axis in the Kerr lens effect 1: Test case with simple source emission near a black hole

We propose a theoretical principle to measure the mass, spin, and direction of spin axis of Kerr black holes (BHs) through observing 2 quantities of the spinning strong gravitational lens effect of BHs. Those observable quantities are generated by 2 light rays emitted at the same time by a source near the BH: the primary and secondary rays that reach a distant observer, respectively, the earliest and secondary temporally. The time delay between detection times and the ratio of observed specific fluxes of those rays are the observable quantities. Rigorously, our proposal is applicable to a single burst-like (short duration) isotropic emission by the source. An extension of our principle to cases of complicated emissions may be constructed by summing up appropriately the result of this paper, which will be treated in future works.

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