Time delay between relativistic images as a probe of cosmic censorship

Abstract

We study the time delay between successive relativistic images in gravitational lensing as a possible discriminator between various collapse end states and hence as a probe of cosmic censorship. Specifically we consider both black hole and naked singularity spacetimes admitting photon spheres where an infinite number of relativistic Einstein Rings can be formed at almost the same radius and naked singularity spacetimes without a photon sphere where multiple relativistic Einstein Rings can form almost up to the center of the lens. The metrics we have considered to sample these scenarios are the Schwarzschild black hole, Janis-Newman-Winicour (naked singularity with photon sphere), Joshi-Malafarina-Narayan, and Tolman-VI (naked singularities without photon sphere) which are a fair sample of the theoretical possibilities.We show that the differential time delay between the relativistic images for naked singularities without a photon sphere progressively decreases for the models we study as opposed to that for black holes and naked singularities with a photon sphere, where it is known to be roughly constant. This characteristic difference in the time delay between successive images for these two cases can be potentially exploited for a source with known intrinsic variability to discriminate between these scenarios even when the images are not spatially resolved.

Strong gravitational lensing by a Konoplya-Zhidenko rotating non-Kerr compact object

“…Finally, we will consider the time delays between the relativistic images, which is another important kind of observables in strong gravitational lensing [76][77][78][79][80]. From the null geodesics equation (12), one has…”

Spacetime Singularities

“…Virbhadra et al 1998, and for recent update and further references, Sahu et al, 2012, 2013. Assuming that a Kerr-like solution of Einstein equations with massless scalar field exists at the center of galaxies, its lensing properties are studied and it was found that there are effects due to the presence of both the rotation and scalar field that would affect the behavior of the bending angle of the light ray, thus making those objects observationally different from black holes (see e.g.…”

Second order Kerr-Newman time delay

“…Gravitational lensing attracts numerous attentions because of its extensive astronomical applications [1][2][3][4][5][6]. Within this geometrical effect, the gravitational time delay of electromagnetic waves acts as one of the most significant parts [7][8][9][10], and has been investigated in detail. The pioneering work of obtaining the first-order gravitational delay of radar echo signals was carried out by Shapiro [11] to test general relativity [12].…”