The instability of naked singularities in the gravitational collapse of a scalar field

One of the fundamental unanswered questions in the general theory of relativity is whether ``naked'' singularities, that is singular events which are visible from infinity, may form with positive probability in the process of gravitational collapse. The conjecture that the answer to this question is in the negative has been called ``cosmic censorship.'' The present paper, which is a continuation previous work, addresses this question in the context of the spherical gravitational collapse of a scalar field.Comment: 35 pages, published version, abstract added in migratio

The Formation of Black Holes in General Relativity

The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first foray into the long time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitably small neighborhood of Minkowskian data. The theorems are general, no symmetry conditions on the initial data being imposed.Comment: 594 pages, 5 figure

Compressible Flow and Euler's Equations

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. We obtain a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there.Comment: 505 page

Blockchain in Academia: Where do we stand and where do we go?

Blockchain is an emerging exponential technology that disrupts the existing way of doing business. During the last 10 years its importance has been highlighted and many organizations worldwide have embraced it and developed innovative applications. Even though Blockchain has been adopted by many sectors, Universities are reluctant to propose new academic programs on this field at bachelor and postgraduate level and fail to efficiently educate students on Blockchain technology and cryptocurrencies. Consequently, universities have failed to investigate the business, technical, legal and other aspects of this technology. As a result, we have the paradox where industry and economy would like to experiment and adopt Blockchain solutions but there is a lack of people with appropriate and adequate skills to work on these solutions. Obviously, this holds back the adoption and the widespread of this technology and currently there are problems in scaling up Blockchain technology. The goal of this paper is to explore the area of Blockchain education and training and propose the structure of a master program that can be used as a model. In doing so, we expand the body of knowledge and we shed light to an important area with limited available information and use cases