Geodesic Structure of Generalized Vaidya Spacetime through the K-Essence

Abstract

This article investigates the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac–Born–Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great detail inside the comoving plane. Indications of the existence of wormholes can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein–Rosen bridge. In addition, we have also detected a distinctive indication of the quantum tunneling phenomenon around the singularity (r→0). Furthermore, we have found that for certain types of solutions, there exist circular orbits through the event horizon as well as quasicircular orbits. Also, we have noted that there is no central singularity in our spacetime where both r and t tend towards zero. The existence of a central singularity is essential for any generalized Vaidya spacetime. This indicates that spacetime can be geodesically complete, which correlates with the findings of Kerr’s recent work (2023).