Gravitational lensing by a massive black hole at the galactic center

There is evidence for a compact 10⁶ M_⊙ object, presumably a black hole, at the Galactic center, close to or coincident with Sgr A*. The characteristic angular scale of gravitational lensing is set by the Einstein ring radius which is ≈20 milli-arcseconds (mas) when the object being lensed is 1 pc beyond Sgr A* at the Galactic center distance of 8.5 kpc. Detection of gravitational lensing on a 10 to 100 mas scale would fix the position of the mass to lie within 1000 AU of Sgr A*, and would constitute strong evidence that the mass is in the form of a black hole. We examine gravitational lensing of the evolved stellar cluster which engulfs Sgr A*, and of Sgr A East, an extended nonthermal source which lies behind Sgr A*. Lensing of the stellar cluster produces a deficit of stellar images within 10 mas of the center, and a surplus between 30 and 300 mas. The surface density of stars is probably too small for detection of this effect. At any given epoch, several faint stars are strongly magnified. The magnification for an individual star lasts for months or years because of stellar proper motion. Both images produced by lensing should be observable and should display transient behavior. Gravitational lensing of substructures associated with Sgr A East (located 10″ in projected distance from Sgr A* and assumed to lie 100 pc beyond) would produce structure on the scale of a few mas in the immediate vicinity of Sgr A*. This structure could be examined by VLBA radio observations provided that there is no intrinsic emission from Sgr A* on this scale.