Particle creation in the marginally bound, self-similar collapse of inhomogeneous dust

Barve, Sukratu; Singh, Tejinder P.; Vaz, Cenalo; Witten, Louis

doi:10.1016/s0550-3213(98)00446-5

Cited by 36 publications

(59 citation statements)

References 67 publications

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“…Hiscock, Williams and Eardley [17] showed the diverging energy flux in the self-similar collapse of a null dust and also calculated the expectation value of stress-energy tensor in its two-dimensional version. Barve et al [18] showed the diverging power of radiation in the self-similar collapse of a dust ball. They also calculated the expectation value of stress-energy tensor in its twodimensional version [19].…”

Section: Introductionmentioning

confidence: 99%

Power, energy, and spectrum of a naked singularity explosion

2000

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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.

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Section: Introductionmentioning

confidence: 99%

Power, energy, and spectrum of a naked singularity explosion

2000

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“…By a simple computation, we can show that A + 4 /A − 4 here is the quantity denoted by γ in Ref. [2]. Hence, we find that the basic property of the map around the singularity is maintained in this new calculation, which does not use any information about the geometry away from the first singular point.…”

Section: Self-similar Casementioning

confidence: 73%

“…This self-similar model was discussed in Ref. [2]. The evolution of the circumferential radius is given by…”

Section: Self-similar Casementioning

confidence: 97%

“…A study of such effects has received some attention in recent years. The most notable feature of these studies is that if a massless scalar field is quantized on the background of a star forming a naked singularity, the outgoing quantum flux of the scalar field can be calculated in the geometric optics approximation [1][2][3][4][5], and in 2-d models [6][7][8]. This quantum flux can be shown to diverge on the Cauchy horizon.…”

Section: Introductionmentioning

confidence: 99%

“…For the self-similar model with a stellar surface on which the background solution is matched to the Schwarzschild metric, this map was determined analytically [2]. It was shown that the map takes the form of a power law : u 0 − u ∝ (v 0 − v) γ , where u = u 0 and v = v 0 are outgoing and incoming null rays passing through the point at which the singularity is first formed.…”

Section: Introductionmentioning

confidence: 99%

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Analytic derivation of the map of null rays passing near a naked singularity

Tanaka

Singh

2001

Phys. Rev. D

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Recently the energy emission from a naked singularity forming in spherical dust collapse has been investigated. This radiation is due to the particle creation in a curved spacetime. In this discussion, the central role is played by the mapping formula between the incoming and the outgoing null coordinates. For the self-similar model, this mapping formula has been derived analytically. But for the model with C ∞ density profile, the mapping formula has been obtained only numerically. In the present paper, we argue that the singular nature of the mapping is determined by the local geometry around the point at which the singularity is first formed. If this is the case, it would be natural to expect that the mapping formula can be derived analytically. In the present paper, we analytically rederive the same mapping formula for the model with C ∞ density profile that has been earlier derived using a numerical technique.

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Midisuperspace Models: Black Hole Collapse

Bojowald

2011

Quantum Cosmology

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Particle creation in the marginally bound, self-similar collapse of inhomogeneous dust

Cited by 36 publications

References 67 publications

Power, energy, and spectrum of a naked singularity explosion

Power, energy, and spectrum of a naked singularity explosion

Analytic derivation of the map of null rays passing near a naked singularity

Midisuperspace Models: Black Hole Collapse

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