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.     

A spherically symmetric gravitational collapse-field with radiation

An interior spherically symmetric solution of Einstein’s field equations corresponding to perfect fluid plus a flowing radiation-field is presented. The physical 3-spacet=constant of our solution is spheroidal. Vaidya’s pure radiation field is taken as the exterior solution. The inward motion of the collapsing boundary surface follows from the equations of fit. An approximation procedure is used to get a generalization of the standard Oppenheimer-Snyder model of collapse with outflow of radiation. One such explicit solution has been given correct to second power of eccentricity of the spheroidal 3-space.     

Strong curvature naked singularities in non-self-similar gravitational collapse

It is shown that strong curvature naked singularities form in a non-self-similar gravitational collapse of radiation. The imploding radiation space-times with a general form of mass function are analyzed and we show that a strong curvature property holds along all families of non-spacelike geodesies terminating at the singularity in past. In view of the strength of singularity and the non-self-similar nature of space-time, we believe this is a very serious counter-example which must be taken into account for any possible formulation of the cosmic censorship hypothesis.This essay received the fourth award from the Gravity Research Foundation, 1991 — Ed.     

Horizons and singularities in static,spherically symmetric spacetimes

We make a thorough study of the regions near finite-order metric-singularity boundaries of static, spherically symmetric spacetimes. After distinguishing curvature singularities from other types of metric breakdown, we examine the eigenvalues of the energy tensor near the singularities for positivity and energy dominance, find the causal class of the t-translation (static) Killing field, and ascertain the presence or absence of timelike, null, and spacelike geodesic incompleteness for each spacetime. For a certain subclass of spacetimes, we also show the completeness of all timelike and spacelike curves despite the superficial failure of the metric.     

The gravitational field of static spherically symmetric bodies

The study of a previously proposed theory of gravitation [Petry, W. (1979).Gen. Rel. Grav.,10, 599; (1981).Ibid,13, 865] is continued. The field equations are given in a simple covariant form. For a perfect fluid with pressure the static spherically symmetric solutions of the gravitation theory are studied. Inertial and gravitational mass are identical. The solutions agree with the corresponding results of the theory of general relativity up to high order in the coupling constant. Under some natural conditions the solutions of a static spherically symmetric body are not singular.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

Entropy change in axial symmetric gravitational collapse

We calculate the entropy changes of an imperfect-fluid gravitational collapsing system in the axial symmetric situation, analyzing a practical example. We conclude that the entropy of the collapsing system decreases at the beginning of the collapse and then increases very near the system's horizon.     

The electrostatic and gravitational field of spherically symmetric objects

The electrostatic and gravitational fields of an extended spherically symmetric object is presented. The limit to a point-like object is discussed for Born-Infeld type of electrodynamics and it is shown, that the extreme Reissner-Nordstrøm field, where no event horizon occurs, is unphysical.