A Note on Geodesics in Hayward Metric

Abstract: We study timelike and null geodesics in a non-singular black hole metric proposed by Hayward. The metric contains an additional length-scale parameter $\ell$ and approaches the Schwarzschild metric at large radii while approaches a constant at small radii so that the singularity is resolved. We tabulate the various critical values of $\ell$ for timelike and null geodesics: the critical values for the existence of horizon, marginally stable circular orbit and photon sphere. We find the photon sphere exists even if the horizon is absent and two marginally stable circular orbits appear if the photon sphere is absent and a stable circular orbit for photons exists for a certain range of $\ell$. We visualize the image of a black hole and find that blight rings appear even if the photon sphere is absent.