Gravitational collapse in Vaidya space-time for Galileon gravity theory

The motive of this work is to study gravitational collapse in Vaidya space-time embedded in Galileon gravity theory. Galileon gravity is in fact an infrared modification of Einstein gravity, which was proposed as a generalization of the four-dimensional effective theory in the DGP brane model. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in the past from the singularity is the basic objective. To point out the existence of a positive trajectory tangent solution, both particular parametric cases (through tabular forms) and wide range contouring process have been applied. Precisely, the equation of state (EoS) in a perfect fluid satisfies a wide range of phenomena: from dust to exotic fluids like dark energy. We have used the EoS parameter, k, to determine the end collapse state in different cosmological eras.