Collapsing scenarios of K-essence generalized Vaidya spacetime under f(R̄,T̄) gravity

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of $f(\bar{R},\bar{T})$ gravity, specifically in K-essence theory. In this study, the Dirac–Born–Infeld type non-standard Lagrangian is used to calculate the emergent metric ${\bar{G}}_{\mu \nu }$, which is not conformally equivalent to the conventional gravitational metric. We use the function $f(\bar{R},\bar{T})$ to reflect the additive nature of the emergent Ricci scalar ($\bar{R}$) and the trace of the emergent energy–momentum tensor ($\bar{T}$). Our study demonstrates that certain choices of $f(\bar{R},\bar{T})$ may result in the existence of a naked singularity caused by gravitational collapse. The alternative $f(\bar{R},\bar{T})$ values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. In addition, when a certain amount of kinetic energy is present in the K-essence scalar field, mass is entirely converted into energy, indicating that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena.