Cosmic Censorship

Dear Colleagues,

Einstein’s gravitational field theory provides the most accurate description of the gravitational field, astrophysics, and cosmology in the range of phenomena outside the quantum regime. Notably, the theory predicts a number of very important phenomena that have now been observed in our universe, including i) the expansion of the universe; ii) the existence of black holes, both massive (millions of solar masses in size) and astrophysical (10 to 100 solar masses in size); and iii) the existence of detectable gravitational radiation. Yet, there exist space–time solutions to Einstein’s equations in which physical phenomena occur that many physicists believe to be physically unrealistic. Examples include the violation of causality in the Taub-NUT and the Godel solutions, and the existence of naked singularities in the negative mass Schwarzschild solutions.

During the 1960s, Roger Penrose proposed two conjectures that addressed the issue of these physically unrealistic solutions to Einstein’s equations. The “Strong Cosmic Censorship Conjecture” says that, generically, the maximal globally hyperbolic development (evolved using Einstein’s equations) of initial data cannot be extended across a Cauchy horizon into a space–time region in which causality fails. The “Weak Cosmic Censorship Conjecture” says that generally in asymptotically flat solutions of Einstein’s equations containing a singularity, an event horizon prevents the observation of that singularity by external observers. Both of these conjectures, as originally stated, involve somewhat imprecise language, notably the statement of properties of “generic solutions”. Genericity is a crucial feature of these conjectures, and consequently formulating them precisely mathematically is a crucial first step towards proving them.

Throughout the half-century since Penrose proposed the two cosmic censorship conjectures, formulating them precisely and proving them has been a major goal of mathematical relativists. There has been especially notable progress during this recent decade towards this goal by a number of researchers. This work has not yet provided a definitive solution to the question of whether the conjectures are in fact true and if so, in which circumstances. However, the articles presented in this special issue show that such resolution is likely to be obtained in the near future, constituting a major step forward in our understanding of the mathematics of general relativity and Einstein’s gravitational field theory.

Prof. Dr. James Isenberg
Guest Editor

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• Singularity
• Cosmic Censorship Conjecture
• Black Hole
• General Relativity
• Differential Geometry