Gravitational Lensing and Proper Motions of Stars Surrounding the Galactic Center

We examine lensing by the black hole in the Galactic center. We use the new photometric data in the infrared to estimate the density of stars in the star cluster surrounding the black hole. We calculate the probability of lensing by the black hole, the rate of the new events and the influence of lensing on the velocity distribution of proper motions of stars. The relative importance of lensing has its maximum at distances ≈10 mas from the star cluster center. The measurement of the proper motion of stars on the scale of ≈3 mas would be necessary to investigate the orbits of stars at distances ≈103rg from the black hole. In principle the deformation of the projected orbit shape by lensing may serve as a way to estimate the angular momentum of the black hole.