Holography, dimensional reduction and the Bekenstein bound

We consider dimensional reduction of the lightlike holography of the covariant entropy bound from D + 1 dimensional geometry of M × S ¹ to the D dimensional geometry M. With a warping factor, the local Bekenstein bound in D + 1 dimensions leads to a more refined form of the bound from the D dimensional view point. With this new local Bekenstein bound, it is quite possible to saturate the lightlike holography even with nonvanishing expansion rate. With a Kaluza-Klein gauge field, the dimensional reduction implies a stronger bound where the energy momentum tensor contribution is replaced by the energy momentum tensor with the electromagnetic contribution subtracted.