The structure of naked singularity in self-similar gravitational collapse

We study the structure and formation of naked singularities in selfsimilar gravitational collapse for an adiabatic perfect fluid. Conditions are obtained for the singularity to be either locally or globally naked and for the families of non-spacelike geodesics to terminate at the singularity in past. This is shown to be a strong curvature naked singularity in a powerful sense and an interesting relationship is pointed out between positivity of energy and occurrence of naked singularity.     

On the occurrence of naked singularity in spherically symmetric gravitational collapse

Generalizing earlier results of [1], we analyze here the spherically symmetric gravitational collapse of a matter cloud with a general form of matter for the formation of a naked singularity. It is shown that this is related basically to the choice of initial data to the Einstein field equations, and would therefore occur in generic situations from regular initial data within the general context considered here, subject to the matter satisfying the weak energy condition. The condition on initial data which leads to the formation of black hole is also characterized.     

The structure of naked singularity in self-similar gravitational collapse: II

Generalizing the results of Joshi and Dwivedi inComm. Math. Phys. 146, 333 (1992), it is pointed out that strong curvature naked singularities could occur in the self-similar gravitational collapse of any form of matter satisfying the weak energy condition for the positivity of mass-energy density.     

A gravitational collapse singularity theorem consistent with black hole evaporation

Letters in Mathematical Physics - The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole...     

Stability of naked singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary C²-mass functionM(r, v) and a C¹-functionh(r, v) (through the corresponding C¹-metric functionν(t, r)), there exist infinitely many choices of energy distribution functionb(r) such that the ’true’ initial data(M, h(r,v)) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a ’big’ subset of the true initial data set, their occurrence is not generic. The terms ’stability’ and ’genericity’ are appropriately defined following the theory of dynamical systems. The particular case of radial pressurep _r (r) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.     

Homoclinic phenomena in the gravitational collapse

A class of Bianchi IX cosmological models is shown to have chaotic gravitational collapse, due to Poincaré's homoclinic phenomena. We can program such models so that for any given positive integer N (N=∞ included) the universe undergoes N non-periodic oscillations (each oscillation requiring a long time) before collapsing. For N=∞ the universe undergoes periodic oscillations.     

Prevention of gravitational collapse

We apply a new theory of gravitation to the question of gravitational collapse to show that collapse is prevented in this theory under very reasonable conditions. This result also extends to prevent ultimate collapse of the Universe.     

Neutrinos from gravitational collapse

Summary A review is made of neutrino fluxes produced by gravitational collapse events (type-II supernovae?). Recent work of Mayle, Wilson and Schramm is used to examine those aspects of neutrino signal which are relatively independent of the collapse model and those aspects which are sensitive to model details. A discussion of the antineutrino background from the integral of all collapse events is also presented.

---

Riassunto Si esaminano i flussi di neutrini prodotti da eventi di collasso gravitazionale (supernovae di tipo II?). Si usa il lavoro recente di Mayle, Wilson e Schramm per esaminare quegli aspetti del segnale del neutrino che sono relativamente indipendenti dal modello del collasso e quegli aspetti che sono sensibili ai dettagli del modello. Si presenta anche una discussione del background di antineutrini dall'integrale di tutti gli eventi di collasso.

---

Резюме Анализируются нейтринные потоки, образованные в результате гравитационного коллапса. Недавняя табота Мейла, Вильсона и Шрамма используется для изучения таких аспектов нейтринного сигнала, которые не зависят от модели коллапса, а также таких аспектов, которые являются чувствительными к деталям модели. Проводится обсужление фона анти-нейтрино, исходя из интеграла всех событий коллапса.

     

Photinos from gravitational collapse

Very light photinos, if they exist, should be produced in a SN explosion. Using the data from SN 1987A we set limits on the masses of selectrons (and squarks), the SUSY particles involved in the production (and diffusion) of photinos in the stellar medium. The bounds obtained are

Full-size image

, where .     

Quantum mechanics of gravitational collapse

A toy model of gravitational collapse in General Relativity is studied. It consists of a spherically symmetric thin shell of dust with a fixed rest mass. The configuration space is the half-axis and the Hamiltonian splits into a differential operator of infinite order (free Hamiltonian) and a Coulomb potential. Harmonic analysis on the half-axis is used to define the free Hamiltonian. For rest masses comparable to, or lower than one Planck mass, the Kato-Rellich theorem is applicable and one self-adjoint extension of the full Hamiltonian is found. A boundary condition for the wave function results whose effect is to keep the shell away from the singularity. This will lead to superposition of states containing both black and white holes.     

Model of internal gravitational collapse

The concept of internal gravitational collapse is introduced, and the metrics associated with an initially collapsing sphere and the collapse of a spherical layer are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 47–50, August, 1974.     

Can quantum gravitational forces stop gravitational collapse?

We consider, in lowest order of the gravitational coupling constant G, the gravitational potential between two neutrons. As we have previously pointed out [1],the quantum (including spin) contributions to the gravitational field dominate for distances smaller than the Compton wavelength of the neutron. At such distances the gravitational force between two neutrons may be repulsive. In particular, the gravitational forces which are analogous to the familiar Darwin and Fermi forces of quantum electrodynamics are capable of stopping gravitational collapse. Our discussion is within the framework of Einstein's theory, but on a microscopic level. We conclude that gravitational collapse may be halted without the necessity of extending Einstein's theory à la Cartan or otherwise.     

Nonadiabatic gravitational collapse in multidimensional spacetime

We extend to higher dimensions an earlier work of Santos regarding junction conditions for a spherical fluid distribution with heat flux and an electromagnetic field. It is observed that the pressure at the surface of distribution does not vanish when the heat flow is present.     

Classical and quantum gravitational collapse

The quantization of a homogeneous isotropic closed Friedmann model filled with an ideal fluid is discussed within the framework of a geometrodynamical approach.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 81–86, May, 1977.The authors wish to express their deep indebtedness to B. A. Lysov and A. V. Borisov for their valuable help in the writing of this paper.