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

Vaidya Spacetime in Brans-Dicke Gravity's Rainbow