Bending of light in modified gravity at large distances

Abstract

We discuss the bending of light in a recent model for gravity at large distances containing a Rindler- type acceleration proposed by Grumiller [Phys. Rev. Lett. 105, 211303 (2010)]. We consider the static, spherically symmetric metric with cosmological constant A and Rindler-like term 2ar presented in this model, and we use the procedure by Rindler and Ishak [W. Rindler and M. Ishak, Phys. Rev. D 76, 043006 (2007).] to obtain the bending angle of light in this metric. Earlier work on light bending in this model by Carloni, Grumiller, and Preis [Phys. Rev. D 83, 124024 (2011)], using the method normally employed for asymptotically flat space-times, led to a conflicting result (caused by the Rindler-like term in the metric) of a bending angle that increases with the distance of closest approach r0 of the light ray from the centrally concentrated spherically symmetric matter distribution. However, when using the alternative approach for light bending in nonasymptotically flat space-times, we show that the linear Rindler-like term produces a small correction to the general relativistic result that is inversely proportional to r0. This will in turn affect the bounds on Rindler acceleration obtained earlier from light bending and casts doubts on the nature of the linear term 2ar in the metric.