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In this paper we study gravitational lensing in the strong field limit from the perspective of cosmic censorship, to investigate whether or not naked singularities, if they exist in nature at all, can be distinguished from black holes. The spacetime we explore from this perspective is the Joshi-MalafarinaNarayan (JMN) metric which represents a spherically symmetric solution to the Einstein field equations with anisotropic pressure and contains a naked singularity at the center. JMN geometry is matched with the Schwarzschild metric to the exterior at a finite radius. This metric was recently shown to be a possible end state of gravitational collapse of a fluid with zero radial pressure. In the presence of the photon sphere, gravitational lensing signature of this spacetime is identical to that of the Schwarzschild black hole with infinitely many relativistic images and Einstein rings, all of them located beyond a certain critical angle from optic axis and the inner relativistic images all clumped together. However, in the absence of the photon sphere, which is the case for a wide range of parameter values in this spacetime, we show that we get finitely many relativistic images and Einstein rings spaced reasonably apart from one another, some of which can be formed inside the critical angle for the corresponding Schwarzschild black hole. This study suggests that the observation of relativistic images and rings might, in principle, allow us to unravel the existence of the naked singularity in the absence of the photon sphere. Also, the results obtained here are in contrast with the earlier investigation on Janis-Newman-Winicour (JNW) naked singularities where it was shown that the radial caustic is always present in the absence the photon sphere, which is not the case with JMN geometry where radial caustic is absent. We also point out the practical difficulties that might be encountered in the observation of the relativistic images and suggest that new dedicated experiments and techniques have to be developed in future for this purpose.

Abstract. We present Cousins R and I band photometry of variable stars in a ∼13 × 13 region in the disk of M 31 galaxy, obtained during 141 nights. Of the 26 Cepheid variables present in the region, two are newly discovered, 11 are classified as Cepheids for the first time and 13 are confirmed as Cepheids. The extensive photometry of these Cepheids enabled us to determine precise phase and amplitude of pulsation which ranges from 0.11 to 0.48 mag in R band. The period of variability ranges from ∼7.5 to 56 days. The period-luminosity diagram is used to derive a distance modulus of 24.49 ± 0.11 mag for M 31 galaxy. We also report variability in 333 other stars, of them, 115 stars appear to be long period variables, 2 suspected eclipsing binaries and remaining 216 are irregular variables.

We study gravitational lensing by a recently proposed black hole solution in loop quantum gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the "mass suppression" effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied, and a sample consistency relation is presented which could serve as a test of this model. We discuss that, though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for a billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.

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We present deep Giant Metrewave Radio Telescope (GMRT) OH and Westerbork Synthesis Radio Telescope (WSRT) H i absorption spectra of the z= 0.6846 gravitational lens toward B0218+357. Both the 1665‐ and 1667‐MHz OH lines are clearly detected for the first time, while a new wide absorption component was detected (at low significance) in the H i spectrum; the OH spectra yielded an OH column density of NOH= 2.3 × 1015 cm−2. The ratio of 1667‐ and 1665‐MHz equivalent widths is ∼1.8 while the redshift of peak OH absorption is z= 0.68468 ± 0.000008 for both lines; this redshift agrees with that obtained from the H i line. The velocity spread (between nulls) of the H i absorption is ∼140 km s−1, while that of both OH lines is ∼100 km s−1; the H i and OH spectra are broadly similar in that they each have two principal narrow components and a wide absorption trough. We argue that the wide absorption is likely to arise from source components in the Einstein ring and derive a rotation velocity of ∼150 km s−1 at a distance of 1.5 kpc from the centre of the z∼ 0.6846 galaxy.