  Due to the exponential high gravitational red shift near the event horizon of
a black hole, it might appears that the Hawking radiation would be highly
sensitive to some unknown high energy physics. To study possible deviations
from the Hawking's prediction, the dispersive field theory models have been
proposed, following the Unruh's hydrodynamic analogue of a black hole
radiation. In the dispersive field theory models, the dispersion relations of
matter fields are modified at high energies, which leads to modifications of
equations of motion. In this paper, we use the Hamilton-Jacobi method to
investigate the dispersive field theory models. The preferred frame is the
static frame of the black hole. The dispersion relation adopted agrees with the
relativistic one at low energies but is modified near the Planck mass $m_{p}$.
We calculate the corrections to the Hawking temperature for massive and charged
particles to $\mathcal{O}\left(m_{p}^{-2}\right) $ and massless and neutral
particles to all orders. Our results suggest that the thermal spectrum of
radiations near horizon is robust, e.g. corrections to the Hawking temperature
are suppressed by $m_{p}$. After the spectrum of radiations near the horizon is
obtained, we use the brick wall model to compute the thermal entropy of a
massless scalar field near the horizon of a 4D spherically symmetric black
hole. We find that the leading term of the entropy depends on how the
dispersion relations of matter fields are modified, while the subleading
logarithmic term does not. Finally, the luminosities of black holes are
computed by using the geometric optics approximation.
