Shadow of Schwarzschild–Tangherlini black holes

摘要

We study the shadow cast by the higher-dimensional Schwarzschild–Tangherlini black hole, and analytically calculate the influence of extra dimensions on the shadow of a black hole. A black hole casts a shadow as an optical appearance because of its strong gravitational field which is known to be a dark zone covered by a circle for a Schwarzschild black hole. We demonstrate that the null geodesic equation can be integrated by Hamilton–Jacobi approach, which enable us to investigate the shadow cast by the higher-dimensional Schwarzschild–Tangherlini black holes. Interestingly, it turns out that, for fixed values of the mass parameter, the shadow in higher-dimensional spacetimes are smaller when compared with four-dimensional Schwarzschild black hole. Further, the shadows of higher-dimensional Schwarzschild–Tangherlini black holes are concentric circles with radius of the circle decreases with increase inD. We visualize the photon regions and the shadows in various dimensions for different values of the parameters, and the energy emission rates are is also investigated. Our results, in the limitD=4, reduced exactly tovis-à-visSchwarzschild black hole case.