Gravitational lensing in the strong field limit

Gravitational lensing is a prediction of General Relativity which has been verified extensively but mostly in weak or moderate gravitational fields. Hence the study of lensing in strong field regime is important not only from the point of view of testing GR vis-a-vis alternatives to it (which by construction have same weak field limit as GR) but also as a probe of various compact object scenarios in GR. We will discuss the importance of photon sphere for strong field lensing and the phenomenon of 'relativistic images'. Earlier, some models such as JNW solution (a naked singularity spacetime with minimally coupled massless scalar field) were studied towards such a purpose. However, it would be useful to investigate a more realistic compact object that forms as end state of gravitational collapse. Lensing in the background of such a model (which is also a Naked Singularity solution) where relativistic images are present even in the absence of photon sphere will be discussed and compared to Schwarzschild Black Hole case. In the presence of photon sphere, one can calculate what are called 'strong lensing coefficients' which can be related to observables in strong lensing limit . We will discuss the formalism and and its application to some cases.