Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities (0710.2333v1)

Abstract: We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for the Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due the Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginally strongly naked singularity lenses always have positive time delays. On the other hand, the strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has negative time delay. We also found that the scalar field decreases the time delay and increases the magnitude of magnifications of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.

• The paper demonstrates that while black holes, weakly and marginally naked singularities produce consistently positive time delays, strongly naked singularities can yield negative delays.
• The authors employ detailed simulation models of the Galactic center to compare lensing features, suggesting that naked singularities may function as more efficient cosmic lenses.
• The study finds that scalar fields in naked singularity models reduce time delays while enhancing image magnifications, offering a potential observational test of cosmic censorship.

Overview of Gravitational Lensing Effects Due to Black Holes and Naked Singularities

The paper of gravitational lensing by massive objects such as black holes (BHs) and naked singularities (NSs) offers critical insights into the structure of spacetime and the distribution of dark matter in galaxies. The paper "Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities" by Virbhadra and Keeton explores this complex topic by modeling the massive dark object at the center of the Galaxy as both a Schwarzschild black hole and as Janis-Newman-Winicour naked singularities. The research focuses on examining gravitational lensing phenomena—specifically, time delay, magnification centroid, and total magnification—produced by these objects.

Summary and Key Findings

The analysis conducted in this paper differentiates the lensing effects of Schwarzschild black holes and various types of naked singularities, characterized as weakly naked singularities (WNS), marginally strongly naked singularities (MSNS), and strongly naked singularities (SNS). The significance of evaluating these distinctions lies in understanding whether naked singularities, which are not shielded by an event horizon, can exist in nature and how they might differ observationally from black holes. The paper delivers crucial findings:

1. Qualitative Differences in Lensing: The SBH, WNS, and MSNS exhibit closely related lensing behaviors. These include positive time delays and similarly positioned Einstein rings, which suggest these objects might be observationally indistinguishable. However, SNS lenses present a stark contrast, producing both positive and negative time delays and different image structures which might allow them to be observationally distinguished from black holes more easily.
2. Time Delay Implications: The paper finds that while images caused by BHs, WNS, and MSNS always yield positive time delays, the same is not true for SNS, which can have positive, zero, or negative time delays. This indicates that if SNSs exist in nature, they could serve as more efficient cosmic telescopes.
3. Impact of Scalar Fields: The scalar field associated with NSs decreases the time delay and increases the magnifications of images relative to Schwarzschild black holes. This effect suggests that NSs could potentially have significant observable consequences in cosmological studies if they exist.
4. Existence of Critical Curves and Caustics: Whereas SBHs, WNSs, and MSNSs do not produce radial caustics, implying a simpler lensing structure, SNSs exhibit these features and can have no or double Einstein rings, pointing toward a much richer and complex lensing geometry.

The paper includes extensive calculations and simulations using updated observational data from the Galactic center, enhancing the reliability of the predictive models used. The results posit that observational facilities, possibly undergoing advancements, might resolve these lensing effects and provide real evidence supporting or disproving the existence of NSs.

Implications and Future Research Directions

The differences identified by the paper carry significant implications for our understanding of general relativity and the potential breakdown of the cosmic censorship hypothesis if SNSs are detected. From a practical astrophysics perspective, naked singularities could, as the paper suggests, be more effective cosmic lenses than black holes, leading to enhanced observational prospects when studying distant cosmic bodies.

Looking forward, detecting and distinguishing the observational signatures implicit in NS lensing could provide direct tests of theoretical predictions related to these exotic objects. Progressive improvements in telescope technologies and computational astrophysics models will be integral in further exploring these relativistic phenomena, potentially leading to breakthroughs in our understanding of fundamental physics.

Thus, Virbhadra and Keeton’s investigation stands as a substantive contribution to both theoretical and observational astrophysics, offering a deeper framework for interpreting gravitational lensing and its role in the universe’s dark structure.