Power, energy, and spectrum of a naked singularity explosion

Abstract

Naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. We show that explosive radiation is emitted during the formation process of the naked singularity. The energy flux is proportional to $(t_{\mathrm{CH}}-t{)}^{-3/2}$ for a minimally coupled massless scalar field, while is proportional to $(t_{\mathrm{CH}}-t{)}^{-1}$ for a conformally coupled massless scalar field, where $t_{\mathrm{CH}}-t$ is the `remained 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 the energy depends on parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is characteristic frequency ${\nu }_s$ of singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wave length is about $t_{\mathrm{CH}}-t$ at each moment. The observed total spectrum is nonthermal, i.e., $\nu dN/d\nu \sim (\nu /{\nu }_s{)}^{-1}$ for $\nu >{\nu }_s$. 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 $10^{54}(M/M_{\odot })$ erg. The calculations are based on the geometrical optics approximation which turns out to be consistent as 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 ultra high energy cosmic rays or a central engine of gamma ray bursts.

34 pages, 13 postscript figures included, to appear in Phys. Rev. D, grammatical errors corrected

References in corpus (5)

• Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --
• Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure
• Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -
• Naked Singularity Explosion
• Gamma-ray bursts as the birth-cries of black holes

Cited by in corpus (22)

• Numerical Approaches to Spacetime Singularities
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Toward a Midisuperspace Quantization of LeMaitre-Tolman-Bondi Collapse Models
• Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity
• Naked singularities and quantum gravity
• High Speed Dynamics of Collapsing Cylindrical Dust Fluid
• Observational Testability of Kerr bound in X-ray Spectrum of Black-Hole Candidates
• Geometry and topology of singularities in spherical dust collapse
• How Does Naked Singularity Look?
• Physical aspects of naked singularity explosion - How does a naked singularity explode? --
• Particle creation in gravitational collapse to a horizonless compact object
• Toward a Quantization of Null Dust Collapse
• Semiclassical Instability of the Cauchy Horizon in Self-Similar Collapse
• Burst particle creation in gravitational collapse to a horizonless compact object
• Hawking temperature for near-equilibrium black holes
• Analytic derivation of the map of null rays passing near a naked singularity
• Visible borders of spacetime generated by high-energy collisions
• Newtonian Analysis of Gravitational Waves from Naked Singularity
• Particle Creation by Naked Singularities in Higher Dimensions
• Energy emission from high curvature region and its backreation
• Naked singularity explosion in higher-dimensional dust collapse
• Naked Singularity Explosion in Higher Dimensions