Constraining the spin and the deformation parameters from the black hole shadow

Abstract

Within 5–10 years, very-long baseline interferometry (VLBI) facilitieswill be able to directly image the accretion flow around SgrA*, thesuper-massive black hole candidate at the center of the Galaxy, and observethe black hole ``shadow''. In 4-dimensional general relativity, the no-hair theoremasserts that uncharged black holes are described by the Kerr solution and arecompletely specified by their mass M and by their spin parameter a. In thispaper, we explore the possibility of distinguishing Kerr and Bardeen black holesfrom their shadow. In Hioki & Maeda (2009), under the assumption that thebackground geometry is described by the Kerr solution, the authors proposedan algorithm to estimate the value of a/M by measuring the distortion parameterδ, an observable quantity that characterizes the shape of the shadow.Here, we try to extend their approach. Since the Hioki-Maeda distortionparameter is degenerate with respect to the spin and possible deviations fromthe Kerr solution, one has to measure another quantity to test the Kerr blackhole hypothesis. We study a few possibilities. We find that it is extremely difficultto distinguish Kerr and Bardeen black holes from the sole observation of theshadow, and out of reach for the near future. The combination of the measurementof the shadow with possible accurate radio observations of a pulsar in a compactorbit around SgrA* could be a more promising strategy to verify the Kerr blackhole paradigm.