The influence of central black holes on gravitational lenses

Recent observations indicate that many if not all galaxies host massive cen tral black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely supp ress the central images for all source positions. Realistic central black h oles are likely to have masses below this critical value. Even in such subc ritical cases, the black hole can suppress the central image when the sourc e is inside a zone of influence, which depends on the core radius and black hole mass. In the subcritical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detecta ble with high-resolution and large dynamic range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.