Black Hole Shadows of Charged Spinning Black Holes

We propose a method for measuring the black hole charge by imaging a black hole shadow in a galactic center by future interferometers. Even when the black hole is uncharged, it is possible to confirm the charge neutrality by this method. We first derive the analytic formulae of the black hole shadow in an optically thin medium around a charged spinning black hole, and then investigate how contours of the black hole shadow depend on the spin and the charge of the black hole for several inclination angles between the rotation axis of the black hole and the observer. This method only assumes stationary black hole and general relativity. By fitting the formula of the contours of the shadow to the observed image of the shadow, in addition to the black hole charge, one can also determine the black hole spin and the inclination angle without any degeneracy among the charge, the spin, and the inclination angle unless the inclination angle is null. If the maximum width of the shadow smaller than 4(1+ 2)M or the minimum width of the shadow smaller than 9M are measured observationally, we can safely conclude that the black hole is charged. Here, M is the gravitational radius, i.e. the half of the Schwarzschild radius.