368 research outputs found
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 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 density profile that has been earlier derived using a
numerical technique.Comment: 4 pages, submitted to Phys. Rev.
Are naked singularites forbidden by the second law of thermodynamics?
By now, many examples of naked singularities in classical general relativity
are known. It may however be that a physical principle over and above the
general theory prevents the occurrence of such singularities in nature.
Assuming the validity of the Weyl curvature hypothesis, we propose that naked
singularities are forbidden by the second law of thermodynamics.Comment: 6 pages, Latex file. This essay was selected for honorable mention by
the Gravity Research Foundatio
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.
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
Spherical gravitational collapse: tangential pressure and related equations of state
We derive an equation for the acceleration of a fluid element in the
spherical gravitational collapse of a bounded compact object made up of an
imperfect fluid. We show that non-singular as well as singular solutions arise
in the collapse of a fluid initially at rest and having only a tangential
pressure. We obtain an exact solution of Einstein equations, in the form of an
infinite series, for collapse under tangential pressure with a linear equation
of state. We show that if a singularity forms in the tangential pressure model,
the conditions for the singularity to be naked are exactly the same as in the
model of dust collapse.Comment: Latex, 26 page
Gravitational Collapse, Black Holes and Naked Singularities
This article gives an elementary review of gravitational collapse and the
cosmic censorship hypothesis. Known models of collapse resulting in the
formation of black holes and naked singularities are summarized. These models,
when taken together, suggest that the censorship hypothesis may not hold in
classical general relativity. The nature of the quantum processes that take
place near a naked singularity, and their possible implication for
observations, is briefly discussed.Comment: 17 pages, Latex File. Based on a talk given at the Discussion
Workshop on Black Holes, Bangalore, 9-12 Dec. 1997, to appear in the
Conference Proceeding
A simple derivation of the naked singularity in spherical dust collapse
We describe a simple method of determining whether the singularity that forms
in the spherically symmetric collapse of inhomogeneous dust is naked or
covered. This derivation considerably simplifies the analysis given in the
earlier literature, while giving the same results as have been obtained before.Comment: Latex, 9 page
Newtonian Analysis of Gravitational Waves from Naked Singularity
Spherical dust collapse generally forms a shell focusing naked singularity at
the symmetric center. This naked singularity is massless. Further the Newtonian
gravitational potential and speed of the dust fluid elements are everywhere
much smaller than unity until the central shell focusing naked singularity
formation if an appropriate initial condition is set up. Although such a
situation is highly relativistic, the analysis by the Newtonian approximation
scheme is available even in the vicinity of the space-time singularity. This
remarkable feature makes the analysis of such singularity formation very easy.
We investigate non-spherical even-parity matter perturbations in this scheme by
complementary using numerical and semi-analytical approaches, and estimate
linear gravitational waves generated in the neighborhood of the naked
singularity by the quadrupole formula. The result shows good agreement with the
relativistic perturbation analysis recently performed by Iguchi et al. The
energy flux of the gravitational waves is finite but the space-time curvature
carried by them diverges.Comment: 23 pages, 8 figure
Can Naked Singularities Yield Gamma Ray Bursts?
Gamma-ray bursts are believed to be the most luminous objects in the
Universe. There has been some suggestion that these arise from quantum
processes around naked singularities. The main problem with this suggestion is
that all known examples of naked singularities are massless and hence there is
effectively no source of energy. It is argued that a globally naked singularity
coupled with quantum processes operating within a distance of the order of
Planck length of the singularity will probably yield energy burst of the order
of M_pc^2\approx2\times 10^{16} ergs, where M_p is the Planck mass.Comment: 4 pages, TeX, no figure
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