Abstract
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.
Highlights
Astrophysical black hole (BH) candidates are compact objects in X-ray binaries with a mass M ≈ 5–20 M and supermassive bodies at the center of galaxies with a mass M ∼ 105 to 1010 M [1]
In the framework of standard physics, the spacetime geometry around these objects should be described by the Kerr solution of general relativity
The two main techniques to probe the spacetime geometry around BH candidates are the study of the thermal spectrum of thin disks [11,12,13] and the analysis of the iron Kα line [14,15]
Summary
Astrophysical black hole (BH) candidates are compact objects in X-ray binaries with a mass M ≈ 5–20 M and supermassive bodies at the center of galaxies with a mass M ∼ 105 to 1010 M [1]. The two main techniques to probe the spacetime geometry around BH candidates are the study of the thermal spectrum of thin disks (continuum-fitting method) [11,12,13] and the analysis of the iron Kα line [14,15] These techniques are normally used to measure the spin parameter of BH candidates under the assumption of the Kerr background, but they can be generalized to non-Kerr metrics to constrain possible deviations from the Kerr solution [16,17,18,19,20,21,22,23,24].
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