The global existence problem and cosmic censorship in general relativity

1981 ◽  
Vol 13 (9) ◽  
pp. 887-892 ◽  
Author(s):  
Vincent Moncrief ◽  
Douglas M. Eardley
Keyword(s):  
General Relativity ◽  
Global Existence ◽  
Cosmic Censorship ◽  
Existence Problem

scholarly journals Space–time singularities and cosmic censorship conjecture: A Review with some thoughts

2020 ◽  
Vol 35 (14) ◽  
pp. 2030007 ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
General Relativity ◽  
Short Review ◽  
Big Bang ◽  
Cosmic Censorship ◽  
Space Time ◽  
Singularity Theorems ◽  
Time Singularities ◽  
The One ◽  
The Big Bang ◽  
Cosmic Censorship Conjecture

The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses that result in the formation of black holes. If singularities — except the one at the Big Bang — ever become “naked,” i.e. not shrouded by black hole horizons, then it is expected that problems would arise and render general relativity indeterministic. For this reason, Penrose proposed the cosmic censorship conjecture, which states that singularities should never be naked. Various counterexamples to the conjecture have since been discovered, but it is still not clear under which kind of physical processes one can expect violation of the conjecture. In this short review, I briefly examine some progresses in space–time singularities and cosmic censorship conjecture. In particular, I shall discuss why we should still care about the conjecture, and whether we should be worried about some of the counterexamples. This is not meant to be a comprehensive review, but rather to give an introduction to the subject, which has recently seen an increase of interest.

Global existence and non-existence problem for a reaction—diffusion equation with a conserved first integral

1995 ◽  
Vol 451 (1943) ◽  
pp. 701-709
Keyword(s):  
Global Existence ◽  
Diffusion Equation ◽  
Finite Time ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
First Integral ◽  
Stationary Solutions ◽  
Reaction Diffusion Equation ◽  
Existence Problem ◽  
Appl Math

In this paper, we prove the global existence and non-existence of solutions of the following problem: RDC{ u t = u xx + u 2 - ∫ u 2 ( x ) d x , x ϵ (0, 1), t > 0, u x (0, t ) = u x (1, t ) = t > 0, u ( x , 0) = u 0 ( x ), x ϵ (0, 1), ∫ 1 0 u ( x, t ) d x = 0, t > 0, Moreover, let u m ( x ) be a stationary solution of problem RDC with m zeros in the interval (0, 1) for m ϵ N , and if we take u 0 ( x ). Then we have that the solution exists globally if 0 < ϵ < 1, and blows up in finite time if ϵ > 1. This result verifies the numerical results of Budd et al . (1993, SIAM Jl appl. Math . 53, 718-742) that the non-zero stationary solutions are unstable.

scholarly journals A Little Quantum Help for Cosmic Censorship and a Step Beyond All That

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Nikolaos Pappas
Keyword(s):  
General Relativity ◽  
Event Horizon ◽  
Crucial Role ◽  
Naked Singularity ◽  
Cosmic Censorship ◽  
Usual Sense ◽  
Naked Singularities ◽  
Open Question ◽  
Heisenberg's Uncertainty Principle ◽  
The Universe

The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the classical (e.g., nonquantum) level. More than 40 years after it was proposed, the validity of the hypothesis remains an open question. We reconsider CCH in both its weak and strong versions, concerning point-like singularities, with respect to the provisions of Heisenberg’s uncertainty principle. We argue that the shielding of the singularities from observers at infinity by an event horizon is also quantum mechanically favored, but ultimately it seems more appropriate to accept that singularities never actually form in the usual sense; thus no naked singularity danger exists in the first place.

The physics of black holes II

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Energy Condition ◽  
Kerr Black Hole ◽  
Cosmic Censorship ◽  
Quantum Field ◽  
Schwarzschild Solution ◽  
Physics Of Black Holes ◽  
Penrose Process ◽  
Cosmic Censorship Hypothesis

This chapter gives a brief description of Hawking radiation, which involves a combination of general relativity and quantum field theory and leads to a thermodynamical interpretation of the laws governing the evolution of black holes. The study of the Penrose process near a Kerr black hole leads to the conclusion that its irreducible mass can only increase. A similar but more general conclusion was reached by Hawking, who showed that the sum of the areas of the horizons of black holes interacting with matter can only increase, with the condition that the cosmic censorship hypothesis is valid and that the matter obeys the so-called weak energy condition. The chapter concludes with the Israel theorem, which allows one to argue that if gravitation is described by general relativity, then not only do black holes exist, but all black holes are represented by the Kerr–Schwarzschild solution.

Finding the Singularity of a Black Hole: Cosmic Censorship Conjecture

2020 ◽  
Vol 29 (12) ◽  
pp. 10-16
Author(s):  
Bogeun GWAK
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Mass Density ◽  
Energy Condition ◽  
Deep Understanding ◽  
Compact Object ◽  
Null Energy Condition ◽  
Cosmic Censorship ◽  
Weak Version ◽  
Cosmic Censorship Conjecture

According to the singularity theorem, a curvature singularity can be formed in a gravitational collapse under the null energy condition. Eventually, the singularity possesses sufficient mass density for the horizon to appear, and the compact object thereby evolves into a black hole. Hence, on the basis of general relativity, the singularity must be located at the center of the black hole. Our curiosity begins here: can we see the singularity? To answer this question, the cosmic censorship conjecture comes into play. That conjecture, which was originally proposed by Penrose, has two versions. The weak version states that a static observer located outside the black hole cannot see the singularity. Furthermore, the strong version states that no observers can see the singularity. Studies regarding the cosmic censorship conjecture are still ongoing, and evidently, its validation requires a deep understanding of the theory of gravity, including general relativity. Herein, we review the progress of studies associated with the weak and the strong cosmic censorship conjectures. Furthermore, we briefly describe the Penrose process for extracting energy from a black hole.

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