2008/10/12 by K. S. Virbhadra · 449 citations
Physics and Astronomy · #Adaptive optics and wavefront sensing #Angular diameter #Astrophysical Phenomena and Observations #Astrophysics #Black hole (networking) #Classical mechanics #Deflection (physics) #Galaxy #General relativity #Gravitation #Gravitational lens #Lens (geology) #Mass ratio #Optics #Physics #Pulsars and Gravitational Waves Research #Redshift #Schwarzschild metric #Schwarzschild radius #Stars #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.79.083004
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 79(8) (American Physical Society) · 26 pages, 12 figures. This work is dedicated to the memory of Professor John A. Wheeler
arxiv created 2008/10/12 · openalex publication_date 2009/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We model massive dark objects at centers of many galaxies as Schwarzschild black hole lenses and study gravitational lensing by them in detail. We show that the ratio of mass of a Schwarzschild lens to the differential time delay between outermost two relativistic images (both of them either on the primary or on the secondary image side) is extremely insensitive to changes in the angular source position as well as the lens-source and lens-observer distances. Therefore, this ratio can be used to obtain very accurate values for masses of black holes at centers of galaxies. Similarly, angular separations between any two relativistic images are also extremely insensitive to changes in the angular source position and the lens-source distance. Therefore, with the known value of mass of a black hole, angular separation between two relativistic images would give a very accurate result for the distance of the black hole. Accuracies in determination of masses and distances of black holes would however depend on accuracies in measurements of differential time delays and angular separations between images. Deflection angles of primary and secondary images as well as effective deflection angles of relativistic images on the secondary image side are always positive. However, the effective deflection angles of relativistic images on the primary image side may be positive, zero, or negative depending on the value of angular source position and the ratio of mass of the lens to its distance. We show that effective deflection angles of relativistic images play significant role in analyzing and understanding strong gravitational field lensing.