Novel features of Schwarzschild-like black hole of Lorentz violating bumblebee gravity

A possible avenue for observing quantum gravity (QG) effects at low energy scales is to introduce spontaneous Lorentz violation (LV) in new models of gravity theories. One such model in the literature is bumblebee gravity yielding Schwarzschild-like black hole and weak field Solar System observations involve LV corrections characterized by the parameter l. Here we first show that these LV corrections have a novel genesis in the conical angle Delta = pi b subtended at the origin of the spacetime of massless bumblebee gravity. Exploiting the resultant asymptotic light deflection angle pi b (-1) as a new input in the exact deflection formula, we next study the strong field lensing properties of the Schwarzschild-like black hole exploring how they differ from those of the Schwarzschild black hole of general relativity. It is shown that the angular image separation and ratio of fluxes could respectively be s similar to e( pi l ) and r similar to e(-pi l ) times those of the Schwarzschild black hole (l = 0). However, the shadow of the Schwarzschild-like black hole is independent of l suggesting that observations of shadow radii cannot reveal QG effects. Finally, we raise an interesting issue about the measurability of the LV corrections caused by strong field lensing. An appendix briefly outlines lensing by the spinning bumblebee black hole.