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

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 $C^{\infty}$ 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 $C^{\infty}$ density profile that has been earlier derived using a numerical technique.Comment: 4 pages, submitted to Phys. Rev.

Depletion of energy from Naked Singular regions during gravitational collapse

A distinguishable and observable physical property of Naked Singular Regions of the spacetime formed during a gravitational collapse has important implications for both experimental and theoretical relativity. We examine here whether energy can escape physically from naked singular regions to reach either a local or a distant observer within the framework of general relativity. We find that in case of imploding null dust collapse scenarios field outgoing singular null geodesics including the cauchy horizon can be immersed between two Vaidya spacetimes as null boundary layers with non vanishing positive energy density. Thus energy can transported from the naked singularity to either a local or a distant observer. And example illustrating that similar considerations can be applied to dust models is given.Comment: 5 pages, 1 EPS figure, revised version accepted for publication in PR

Quantum general relativity and Hawking radiation

In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around a black hole, and show that in the WKB approximation, the wave-functional describes an eternal black hole in equilibrium with a thermal bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para following Eqn. (10). Revised version to appear in Phys. Rev.

Can we see naked singularities?

We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence for proving or disproving CCC the study of timelike naked singularities will be more important. Our results are very general and are independent of initial data and the form of the matter.Comment: 10 page

Divergence of the Quantum Stress Tensor on the Cauchy Horizon in 2-d Dust Collapse

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-selfsimilar Tolman Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular co-ordinates in the corresponding four dimensional spherical model.Comment: 16 pages, no figures, LaTeX fil

Efficacy of selection in sexually breeding Artemia (Artemia franciscana, Kellogg, 1906)

Bi-directional selection for smaller naupliar size (SNS) and bigger naupliar size (BNS) was practiced to develop two divergent lines. The e⁄cacy of bidirectional mass selection in Artemia franciscana was evaluated by comparing the predicted genetic gains with the realized genetic gains. Two sets of predictions were made using two heritability estimates, e.g., the heritability estimate from full-sib analysis (h2) and the estimate from regression of o¡spring on mid parent (bop). Predictions with the full-sib heritabilities were of very high magnitude as compared with predictions with bop heritabilities

Learning with a Drifting Target Concept

We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates

Phenotypic estimates and heritability values of Artemia franciscana

Artemia, in all stages of its life cycle, is suitable food for most diversi¢ed groups of aquatic animals. Although its size at different stages restricts its use as a food for some groups of ¢sh, this problem can be overcome using selective breeding techniques. The formulation of any selective breeding programme calls for a proper understanding of the genetic architecture of the economically important traits of the population under study. Thus, heritability for certain important life history and reproductive traits was estimated in Artemia franciscana from the Great Salt Lake, Utah. In the present study, the sexwise heritability values for growth and reproduction traits were estimated using parent offspring regression. The phenotypic parameters for the same traits are also recorded. The naupliar length was 487.072.0 and 490.671.8 mm for males and females, respectively, whereas the heritability values for naupliar length were 0.585170.2153 and 0.376670.1899 respectively. The length at 3 and 6 days of age were 1.8770.03 and 4.1070.08mm, respectively, for maleswhereas1.8770.03 and 4.3070.08mm, respectively, for females.The heritability values for length at 3 and 6 days of age for males were 0.327270.3651 and 0.496570.2466, respectively, whereas the respective values for the females were 0.116770.3841 and 0.022270.2971. The estimates of length at ¢rst brood, pre-reproductive period and number of o¡- spring in ¢rst brood were 10.0970.23mm, 16.007 0.23 days and 53.5771.37 days, respectively, whereas the heritability values for respective traits were 0.040370.1078,0.323470.2874 and 0.340470.2202

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation 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.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a Rapid Communicatio

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.Comment: 18 pages, 16 figure