In this paper we examine the relativistic Einstein rings assuming a nonminimal coupling between gravitation and electromagnetism in a Reissner–Norström background. Starting from a general action of a nonminimal coupled electrodynamics we show that an unstable effective photon sphere may be obtained in the regime of eikonal approximation. Restricting ourselves to the unstable photon sphere domain we examine the expected angular positions of the first and second relativistic Einstein rings. To compare our results with previous studies in the literature we model the lens as a Galactic supermassive black hole. For fixed coupling parameters we show that such angular positions decrease as the charge parameter increases. The angular separation between the first and second rings is also evaluated. We show that such separation increases as the charge parameter increases. These patterns are not followed by nearly extremal configurations. In this case we show that there is an overlap domain so that the angular position and the corresponding coupling parameter do not allow one to differ extremal cases from complementary configurations which satisfy the cosmic censorship hypothesis.

Brazil

Rodrigo Maier

Relativistic Einstein rings of Reissner–Nordström black holes nonminimally coupled to electrodynamics

We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the  $$f(\mathcal {R})=\mathcal {R}+\lambda \mathcal {R}^2$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>λ</mi> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </mrow> </math>   Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.

Fernanda Silveira

Santiago Perez Bergliaffa

A model of compact and ultracompact objects in  $$f(\mathcal {R})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </math>  -Palatini theory