Persistent curvature and cosmic censorship

A definition is given which quantifies the strength of persistent Riemann curvature along a null geodesic. A numerical value thereof is identified which ensures the existence of conjugate points on null geodesics of infinite length. A class of examples show that no lesser value can suffice. One is led to a new theorem of cosmic censorship which identifies an upper bound on the persistent curvature strength with which any space-time may violate weak cosmic censorship. All previous theorems are superceded. Moreover an improved logical construction simplifies interpretation.     

Note on cosmic censorship

A number of recent theorems by Królak and Newman purport to prove cosmic censorship by showing that strong curvature singularities must be hidden behind horizons. I prove that Newman's null, strong curvature condition, which he imposes on certain classes of null geodesics to restrict curvature growth in the space-time, does not hold in many physically realistic space-times: it is not satisfied by any null geodesic in the relevant class in any open Friedmann cosmological model, nor does it hold for any null geodesic in the relevant class in maximal Schwarzschild space. More generally, I argue that the singularity predicted by the Penrose singularity theorem is unlikely to be of the type eliminated by Newman. Thus the Newman theorems are probably without physical significance. The Królak theorems, although based on a physically significant definition of strong curvature singularity, are mathematically invalid, and his approach cannot be used to obtain a cosmic censorship theorem.     

Magnetic charge,black holes,and cosmic censorship

The possibility of converting a Reissner-Nordström black hole into a naked singularity by means of test particle accretion is considered. The dually charged Reissner-Nordström metric describes a black hole only when M² > Q³ + P². The test particle equations of motion are shown to allow test particles with arbitrarily large magnetic charge/mass ratios to fall radially into electrically charged black holes. To determine the nature of the final state (black hole or naked singularity) an exact solution of Einstein's equations representing a spherical shell of magnetically charged dust falling into an electrically charged black hole is studied. Naked singularities are never formed so long as the weak energy condition is obeyed by the infalling matter. The differences between the spherical shell model and an infalling point test particle are examined and discussed.     

Naked singularities cannot be observed (An information-theoretic approach to the cosmic censorship conjecture)

In this article we review some recent results obtained in the interplay between field theory in curved space-time and information theory, and explore some consequences. We shall explain how the Weyl tensor becomes responsible for the creation of quantum noise which, in turn, degrades a considerable fraction of the information which is optically transferred in a curved space-time. We conclude that causal connection between spacetime regions, although being a necessary condition for transmitting information between them, is by no means sufficient. This is because this quantum noise might preclude the observation of very distant objects in the Universe and even closer ones if it becomes very intense. We argue that naked singularities are very powerful sources of noise and, therefore, cannot be observed optically. This leads to the intriguing possibility that the no-hair theorem might be more general than was thought before.     

Gauge theories,black hole evaporation and cosmic censorship

Recent work of Linde, which suggests that gauge theories modify the effective gravitational constant, are applied to the theory of black hole evaporation. Considerable modification of the late stages of evaporation are predicted. Contrary to expectations, the black hole never attains a sufficient temperature to enter the “antigravity” regime, which would represent a failure of cosmic censorship.     

Black holes and the weak cosmic censorship

A theory of black holes is developed under the assumption of the weak cosmic censorship. It includes Hawking's theory of black holes in the future asymptotically predictable spacetimes as a special case but it also applies to the cosmological situations including models with nonzero cosmological constant of both signs.     

Black holes and the strong cosmic censorship

The theory of black holes developed by Hawking in asymptotically flat space-times is generalized so that black holes in the cosmological situations are included. It is assumed that the strong version of the Penrose cosmic censorship hypothesis holds.Part of a Ph.D. thesis submitted to the Physics Faculty of the Warsaw University.     

Finding a statement of cosmic censorship

We consider possible mathematical formulations of the idea that gravitational collapse cannot result in the formation of naked singularities.National Science Foundation predoctoral fellow.     

Singularities,trapped sets,and cosmic censorship in asymptotically flat space-times

We show that space-time is future asymptotically predictable from a regular partial Cauchy provided that singularities are causally preceded by trapped sets. Future asymptotic predictability is a formal statement of cosmic censorship in asymptotically flat space-times. A regular partial Cauchy surface means that singularities in gravitational collapse can arise only from regular initial data. Our result confirms a supposition by Hawking that singularities forced by singularity theorems cannot be naked.     

Classical and quantum models of strong cosmic censorship

The cosmic censorship conjecture states that naked singularities should not evolve from regular initial conditions in general relativity. In its strong form the conjecture asserts that space-times with Cauchy horizons must always be unstable and thus that thegeneric solution of Einstein's equations must be inextendible beyond its maximal Cauchy development. In this paper we shall show that one can construct an infinite-dimensional family ofextendible cosmological solutions similar to Taub-NUT space-time. However, we shall also show that each of these solutions is unstable in precisely the way demanded by strong cosmic censorship. Finally we show that quantum fluctuations in the metric always provide (though in an unexpectedly subtle way) the “generic perturbations” which destroy the Cauchy horizons in these models.     

A proof of the cosmic censorship hypothesis

It is shown that in a weakly asymptotically simple and empty space, according to classical general relativity, from nonsingular initial data no strong curvature singularity can arise that is visible from infinity.This essay received the Second Award from the Gravity Research Foundation for the year 1982. Ed. This work is supported by Interdisciplinary Research Project MR-I-7.