  We consider asymmetrically warped brane models, or equivalently brane models
where the background metric is characterized by different time and space warp
factors. The main feature of these models is that 4D Lorentz symmetry is
violated for fields which propagate in the bulk, such as gravitons. In this
paper we examine the case of bulk photons in asymmetrically warped brane
models. Although our results are general, we examine here two specific but
characteristic solutions: 1) AdS-Schwarzschild 5D Black Hole solution and 2)
AdS-Reissner Nordstrom 5D Black Hole solution. We show that the standard
Lorentz invariant dispersion relation for 4D photons is corrected by nonlinear
terms which lead to an Energy-dependent speed of light. Specifically, we obtain
a sub-luminous Energy-dependent refractive index of the form
n_{eff}(\omega)=1+c_{G} \omega^2, where \omega is the energy of the photon, and
the factor c_G is always positive and depends on the free parameters of the
model. Finally, comparing the results with recent data from the MAGIC
Telescope, claiming a delayed arrival of photons from the Active Galactic
Nucleus of Mk501, we impose concrete restrictions to the two sets of models
examined in this work. We shall also discuss briefly other possible
astrophysical constraints on our models.
