Strong field limit of black hole gravitational lensing.

*(English)*Zbl 1009.83027The authors of this very interesting paper investigate a new formulation of the gravitational lensing theory in the strong field limit for a Schwarzschild black hole as a counterpart to the weak field approach. It is given the geometrical configuration of gravitational lensing, that is, the light emitted by the source \(S\) is deviated by the black hole and reaches the observer. The black hole is defined as any compact object having a radius comparable to its Schwarzschild radius, so that even very compact object which has not undergone a full gravitational collapse would have a similar behavior. Starting from the black hole lens equation (studied by Virbhadra and Ellis (2000)) the authors perform a set of expansions exploiting the source-lens-observer geometry and the properties of highly deflected light rays. They manage to solve the lens equation and find analytical expressions for the infinite set of images formed by the black hole. This interesting approach leads to extremely simple formulae which allow an immediate comprehension of the problem and a straight-forward application to the physically interesting situations. This strong field approach can be considered as the direct counterpart of the weak field limit for its striking simplicity. The position of additional critical curves, relativistic images and their magnification, arising in a strong field limit at a high accuracy degree is discussed.

Reviewer: Dimitar A.Kolev (Sofia)

##### MSC:

83C57 | Black holes |

83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |

83C40 | Gravitational energy and conservation laws; groups of motions |

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\textit{V. Bozza} et al., Gen. Relativ. Gravitation 33, No. 9, 1535--1548 (2001; Zbl 1009.83027)

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