Shadows of CPR black holes and tests of the Kerr metric

We study the shadow of the Cardoso–Pani–Rico black hole for different values of the black hole spin $$a_*$$ , the deformation parameters $$\epsilon _3^t$$ and $$\epsilon _3^r$$ , and the viewing angle i. We find that the main impact of the deformation parameter $$\epsilon _3^t$$ is the change of the size of the shadow, while the deformation parameter $$\epsilon _3^r$$ affects the shape of its boundary. In general, it is impossible to test the Kerr metric, because the shadow of a Kerr black hole can be reproduced quite well by a black hole with non-vanishing $$\epsilon _3^t$$ or $$\epsilon _3^r$$ . Deviations from the Kerr geometry could be constrained in the presence of high quality data and in the favorable case of a black hole with high values of $$a_*$$ and i. However, the shadows of some black holes with non-vanishing $$\epsilon _3^r$$ present peculiar features and the possible detection of these shadows could unambiguously distinguish these objects from the standard Kerr black holes of general relativity.

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