  Doubly special relativity (DSR) is an effective model for encoding quantum
gravity in flat spacetime. To incorporate DSR into general relativity, one
could use "Gravity's rainbow", where the spacetime background felt by a test
particle would depend on its energy. In this scenario, one could rewrite the
rainbow metric $g_{\mu\nu}\left( E\right) $ in terms of some orthonormal frame
fields and use the modified equivalence principle to determine the energy
dependence of $g_{\mu\nu}\left( E\right) $. Obviously, the form of
$g_{\mu\nu}\left( E\right) $ depends on the choice of the orthonormal frame.
For a static black hole, there are two natural orthonormal frames, the static
one hovering above it and freely falling one along geodesics. The cases with
the static orthonormal frame have been extensively studied by many authors. The
aim of this paper is to investigate properties of rainbow black holes in the
scenario with the free-fall orthonormal frame. We first derive the metric of
rainbow black holes and their Hawking temperatures in this free-fall scenario.
Then, the thermodynamics of a rainbow Schwarzschild black hole is studied.
Finally, we use the brick wall model to compute the thermal entropy of a
massless scalar field near the horizon of a Schwarzschild rainbow black hole in
this free-fall scenario.
