Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest radius at which a relativistic image might be formed. For horizonless ultracompact objects, additional relativistic images and rings can form inside this radius. In this paper, we provide an analytical approach to deal with strong gravitational lensing from such ultracompact objects, which is substantially different from the black hole cases, first reported by Bozza. Here, our analysis indicates that the angular separations and magnifications of relativistic images inside the unstable light ring (photon sphere) might be several orders of magnitude higher compared to the ones outside it. This indicates fundamental differences in the nature of strong gravitational lensing from black holes and ultracompact objects.

The recent observation of the shadow of the supermassive compact object M87* by the Event Horizon Telescope (EHT) collaboration has opened up a new window to probe the strong gravity regime. In this paper, we study shadows cast by two viable alternatives to the Kerr black hole, and compare them with the shadow of M87*. The first alternative is a horizonless compact object (HCO) having radius r₀ and exterior Kerr geometry. The second one is a rotating generalization of the recently obtained one parameter (r₀) static metric by Simpson and Visser. This latter metric, constructed by using the Newman-Janis algorithm, is a special case of a parametrised rotating non-Kerr geometry obtained by Johannsen. Here, we constrain the parameter r₀ of these alternatives using the results from M87* observation. We find that, for the mass, inclination angle and the angular diameter of the shadow of M87* reported by the EHT collaboration, the maximum value of the parameter r₀ must be in the range 2.54r₊ ≤ r_{0, max} ≤ 3.51r₊ for the dimensionless spin range 0.5 ≤ a_* ≤ 0.94, with r₊ being the outer horizon radius of the Kerr black hole at the corresponding spin value. We conclude that these black hole alternatives having r₀ below this maximum range (i.e. r₀ ≤ r_{0, max}) is consistent with the size and deviation from circularity of the observed shadow of M87*.

We consider charged black holes in four-dimensional anti–de Sitter space, in the presence of a Weyl correction. We obtain the solution including the effect of backreaction, perturbatively up to first order in the Weyl coupling, and study its thermodynamic properties. This is complemented by a calculation of the holographic entanglement entropy of the boundary theory. The consistency of results obtained from both computations is established.