  In this note we study an energy dependent deformation of a time dependent
geometry in the background of Brans-Dicke gravity theory. The study is
performed using the gravity's rainbow formalism. We compute the field equations
in Brans-Dicke gravity's rainbow using Vaidya metric which is a time dependent
geometry. We study a star collapsing under such conditions. Our prime objective
is to determine the nature of singularity formed as a result of gravitational
collapse and its strength. The idea is to test the validity of the cosmic
censorship hypothesis for our model. We have also studied the effect of such a
deformation on the thermalization process. In this regard we have calculated
the important thermodynamical quantities such as thermalization temperature,
Helmholtz free energy, specific heat and analyzed the behavior of such
quantities.
