Collapsing scenario for the k-essence emergent generalized Vaidya spacetime in the context of massive gravity's rainbow

Abstract

In this study, we investigate the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric closely resembles the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse, where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is also different. This new type k-essence emergent Vaidya massive gravity rainbow metric satisfies the required energy conditions. The existence of a locally naked central singularity and the strength and strongness of the singularities for the rainbow deformations of the k-essence emergent Vaidya massive gravity metric are the interesting outcomes of the present work.