A scan of f(R) models admitting Rindler type acceleration

Abstract: As a manifestation of large distance effect Grumiller modified Schwarzschild metric with an extraneous term reminiscent of Rindler acceleration. Such a term has the potential to explain the observed flat rotation curves in general relativity. The same idea has been extended herein to the larger arena of $f\left( R\right)$ theory. With particular emphasis on weak energy conditions (WECs) for a fluid we present various classes of $f\left( R\right)$ theories admitting a Rindler-type acceleration in the metric.