Power, energy, and spectrum of a naked singularity explosion

Abstract

It is well known that a naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. In this paper we show that explosive radiation is emitted during the formation process of the naked singularity while we fix the background spacetime. The energy flux is proportional to (tCH − t) −3/2 for a minimally coupled massless scalar field, while it is proportional to (tCH − t) −1 for a conformally coupled massless scalar field, where tCH − t is the "remaineing time" until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and energy depends on the parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is a characteristic frequency νs of the singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wavelength is about tCH − t at each moment. The observed total spectrum is nonthermal, i.e., νdN/dν ∼ (ν/νs) −1 for ν > νs. If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about 10 54 (M/M⊙)erg. The calculations are based on the geometrical optics approximation which turns out to be consistent for a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultrahigh energy cosmic rays or a central engine of γ-ray bursts.

Observational testability of a Kerr bound in the x-ray spectrum of black hole candidates

“…Before this study, there are a lot of past studies about the observational feasibility of the super-spinning objects and/or naked singularity in a variety of astrophysical contexts such as; direct radio observations of a super-spinning Kerr object [4,29], accretion disc around a super-spinning Kerr object [64], gravitational lensing phenomena by a superspinning Kerr object [65,66,67,68], light rays from a forming naked singularity [69,70], particle creation (emission) from a forming naked singularity [59,60,61,62,71,72], gravitational radiation from a forming naked singularity [73,74,75,76], physical processes in naked singularity formation [63,77,78], connection to gamma-ray bursts (GRBs) [79,80].…”

Convergence to a self-similar solution in general relativistic gravitational collapse

“…Even for such an "approximate" naked singularity, it has been shown that explosive radiation is emitted due to quantum effects [36][37][38][39][40][41][42][43]. Furthermore, in a practical sense, if the curvature scale reaches the Planck scale, it should be regarded as a singularity because it is considered beyond the scope of classical general relativity.…”

“…, (2.37) 38) and 39) where C k is a constant determined by k as 40) and the parameter D is defined as…”

Particle creation in gravitational collapse to a horizonless compact object

“…at past null infinity as an initial quantum state. Then, the function κ(u) determines radiation power regularized at future null infinity, through [20,26,32]…”