A time-dependent spacetime in f(R,T) gravity: Gravitational collapse

Abstract

In this note, a time-dependent spacetime is explored in the background of [Formula: see text] gravity via the gravitational collapse of a massive star. The star is modeled by the Vaidya spacetime which is time-dependent in nature. The coupling of matter with curvature is the key feature of [Formula: see text] theory and here we have investigated its effects on a collapsing scenario. Two different types of models, one involving minimal and the other involving nonminimal coupling between matter and curvature are considered for our study. Power law and exponential functionalities are considered as examples to check the outcome of the gravitational collapse. A detailed analysis on the appearance of horizons in Vaidya spacetime is performed and its astrophysical implications are explored. Our prime objective is to explore the nature of singularities (black hole or naked singularity) that form as an end state of the collapse. Existence of outgoing radial null geodesics from the central singularity was probed and such existence implied the formation of naked singularities thus defying the cosmic censorship hypothesis. The absence of such outgoing null geodesics would imply the formation of an event horizon and the singularity formed becomes a black hole. Conditions under which such possibilities occur are derived for all the models and sub-models. Gravitational strength of the singularity is also investigated and the conditions under which we can get a strong or a weak singularity is derived. The results obtained are very interesting and may be attributed to the coupling between curvature and matter. It is seen that for nonminimal coupling there is a possibility of a globally naked singularity, whereas for a minimal coupling scenario local nakedness is the only option. It is also found that the singularity formed can be sufficiently weak in nature, which is cosmologically desirable.