Abstract
AbstractA Vaidya spacetime is considered for gravitational collapse of a type II fluid in the context of the Rastall theory of gravity. For a linear equation of state for the fluid profiles, the conditions under which the dynamical evolution of the collapse can give rise to the formation of a naked singularity are examined. It is shown that depending on the model parameters, strong curvature, naked singularities would arise as exact solutions to the Rastall's field equations. The allowed values of these parameters satisfy certain conditions on the physical reliability, nakedness, and the curvature strength of the singularity. It turns out that Rastall gravity, in comparison to general relativity, provides a wider class of physically reasonable spacetimes that admit both locally and globally naked singularities.
Highlights
Since the mid-1970s when the singularity theorems were introduced by Hawking and Penrose [1], the study of gravitational collapse and its final outcome has attracted a great interest in the theories of gravity and relativistic astrophysics
Most of the modified theories of gravity are described by a divergence-free energy-momentum tensor (EMT) which couples to the geometry in a minimal way [78, 79]
Since the Rastall parameter can be interpreted as a measure of non-conservation of the EMT, or in view of Eq (2.2) as the strength of the mutual interaction between the geometry and matter, one can intuitively imagine that such a non-conservation goes in favor of a naked singularity formation rather than a black hole formation
Summary
Despite the arbitrariness of the functions F1(v) and M (v) in our solution (2.11), they should be chosen carefully so that the mass function m(r, v) provides a physically reasonable EMT (2.13) satisfying certain conditions on positivity of matter energy density and its dominance over the pressure. These requirements which are conventionally referred to as energy conditions are summarized as weak, null, strong and dominant energy conditions.
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