Relativistic images of Schwarzschild black hole lensing (0810.2109v1)

Abstract: 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.

• The paper demonstrates that the ratio of black hole mass to differential time delay remains nearly constant, enabling precise mass measurements.
• It employs analytical and numerical models to explore angular positions, magnifications, and deflection angles in weak and strong gravitational fields.
• Findings imply that observing demagnified relativistic images from aligned systems could powerfully test general relativity in strong field regimes.

Overview of "Relativistic images of Schwarzschild black hole lensing"

The paper by K.S. Virbhadra presents a detailed paper of gravitational lensing by Schwarzschild black holes, emphasizing the formation of relativistic images. The paper models massive dark objects (MDOs) at galactic centers as Schwarzschild black holes and tackles the intricacies of gravitational lensing in both weak and strong gravitational fields. The paper outlines that the ratio of the mass of a black hole lens to the differential time delay between two outermost relativistic images is notably stable against variations in angular source position and relative distances between lens, source, and observer. This key constant can thus be leveraged to ascertain precise masses of black holes.

Key Results and Analysis

The paper details the behavior of angular positions, magnifications, and time delays of both primary-secondary image pairs and relativistic images, defined as those forming due to light deflection angles exceeding $3\pi/2$. A notable finding is that angular positions of relativistic images are highly invariant to changes in angular source position and distances, underscoring their potential utility in accurate gravitational measurements. The effective deflection angles of relativistic images are shown to provide substantial insight and are essential for understanding strong-field lensing dynamics.

For cases where lens components are highly aligned, or $\beta$ is small, the demagnified relativistic images become potential observational candidates, particularly for sources such as supernovae that occur near the galactic centers. These images could help test the general theory of relativity in strong-field regimes and consolidate interpretations of MDOs as black holes. Furthermore, the discovery of relativistic images could push forward our limits of optical technology and offer potential new avenues for testing quantum gravity theories.

The analytical insights and numerical evaluations indicate that for nearly orthogonal lens configurations, the angular separations and magnifications of relativistic images show marginal sensitivity to lens-source distance, offering robust avenues for mass and distance estimations once these observations become technologically feasible.

Implications and Future Directions

The paper's findings propose a firm foundation for pursuing Gravitation Lensing as a method for astrophysical measurements and suggest that with advancing observational technologies, relativistic images might become observable, providing insights into compact objects. The demonstrated method for calculating accurate mass and distance metrics using lensing parameters suggests future astronomical endeavors could refine these techniques for enhanced precision.

A significant contribution of the paper is the notion that relativistic images maintain consistent behaviors irrespective of changes in certain parameters, which addresses previous computational limitations and demystifies complex light-matter interactions within strong gravitational fields.

Research stemming from this work would focus on observational strategies for relativistic images, enhancements in statistical and measurement techniques, and the extension of these methodologies to different spacetime geometries such as those around rotating black holes. Additionally, the paper reiterates the relevance of thorough verification and expansion of lens models to encompass phenomena not fully addressed, such as gravitational retro-lensing and lensing disparities between black holes and naked singularities.

Overall, the work of Virbhadra serves as a comprehensive exploration of relativistic lensing by Schwarzschild black holes, offering theoretical predictions that can be of substantial value as gravitational lensing technologies and methods continue to evolve.