Gravitational collapse and naked singularities

Abstract

Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for researches in this field. In the absence of general proof for the censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent development has revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of ``effective naked singularities'', which will be quite helpful because general relativity has the limitation of its application for high-energy end. The appearance of naked singularities is not detestable but can open a window for new physics of strongly curved spacetimes.Comment: 12 pages, to appear in the Proceedings of the International Conference on Gravitation and Cosmology (ICGC-2004), ed. by B.R. Iyer, V. Kuriakose and C.V. Vishveshwara, published by Pramana, minor correction

Can We See Naked Singularities?

“…Our assumptions are most natural and typically we want them to hold for any physically relevant case. All the earlier known cases [3,4,5,6,7,8,9,10,11,12,13,14] of naked singularities in spherically symmetric gravitational collapse of type I matter field fall under our analysis. Our result is based only on local analysis of some Einstein equations and geodesic equations near the central singularity.…”

“…Proving or disproving CCC is one of the most important open problems in general relativity and black hole physics. There are many specific examples of naked singularities as well as many cases directly or indirectly supporting the conjecture [3,4,5,6,7,8,9,10,11,12,13,14,15]. Most of these studies are based on showing the existence of the outgoing radial null geodesics (ORNGs) from the singularity.…”

Naked singularity formation in $${f({\mathcal R})}$$ gravity

“…Such a behavior was discovered in gravitational collapse of a spherically symmetric massless scalar field [31], axisymmetric gravitational waves [32], spherical system of a radiation fluid [33] and spherical system of a perfect fluid obeying the equation of state p = wρ [34]. Consider a type II critical collapse in which the black hole mass is scaled as M BH ∝| p − p * | γ , where p parameterizes a family of initial data sets evolving through Einstein's equations, p * is a critical value and γ is a positive constant which is called a critical exponent [30,35]. For a sufficiently large value of p the collapse procedure develops to a black hole and for a sufficiently small one it evolves to a dispersion [35].…”

“…Consider a type II critical collapse in which the black hole mass is scaled as M BH ∝| p − p * | γ , where p parameterizes a family of initial data sets evolving through Einstein's equations, p * is a critical value and γ is a positive constant which is called a critical exponent [30,35]. For a sufficiently large value of p the collapse procedure develops to a black hole and for a sufficiently small one it evolves to a dispersion [35]. The boundary between these two regimes is the black hole threshold.…”

“…In such a limit, the black hole mass tends to zero and the maximum value of curvature diverges just outside the event horizon. Since we have arbitrarily strong curvature outside the event horizon by fine-tuning, the black hole threshold can be regarded as a globally naked singularity [35]. Let us now consider the geometry of the exterior spacetime.…”