Singularity resolution in gravitational collapse

Abstract

We investigate the unhindered gravitational collapse of a homogeneous scalar field with nonzero potential, a two-dimensional analog of the Mexican hat-shaped Higgs field potential. We prove that the density dependence on the scale factor cannot be expressed as an algebraic function in such a scenario. For a certain transcendental expression of the density of such field as a function of scale factor, we then show that the collapse evolves to a singularity at an infinite comoving time, which is equivalent to saying that the singularity is avoided altogether. An ultra high density region (UHDR) of the order of Planck length can, however, be reached in a finite comoving time. The absence of the formation of trapped surfaces makes this UHDR globally visible.

Gravitational Collapse of Massless Vector Field with Positive Cosmological Constant

“…with equation ( 16) implying the positivity of the above equation (17). The expansion scalar is positive (i.e., θ l > 0) when a(t), if it satisfies the following equation,…”

“…The context of visibility of singularities formed by gravitational collapse has gained much interest and importance in recent times [5][6][7][8][9][10][11][12][13][14][15][16][17]. It has been shown that dust clouds having a minimum or sufficient inhomogeneity collapsing spherically can result in the formation of a Naked Singularity (NS) where null geodesics can escape the trapped surfaces and reach distant observers, thus being visible to them [18][19] The prime reason being that if these spacetime singularities are visible to a distant observer, the visible null geodesics would bear the possible physical and detectable signatures of quantum effects (of gravity) which are expected to have strong impacts in the region of ultra-strong gravitational fields and thus providing us with the much needed insights on the physical effects of quantum gravity on a spacetime manifold.…”