Developments in General Relativity: Black Hole Singularity and Beyond

At the 20-th Texas Symposium on Relativistic Astrophysics there was a plenary talk devoted to the recent developments in classical Relativity. In that talk the problems of gravitational collapse, collisions of black holes, and of black holes as celestial bodies were discussed. But probably the problems of the internal structure of black holes are a real great challenge. In my talk I want to outline the recent achievements in our understanding of the nature of the singularity (and beyond!) inside a realistic rotating black hole. This presentation also addresses the following questions: Can we see what happens inside a black hole? Can a falling observer cross the singularity without being crushed? An answer to these questions is probably "yes".Comment: 13 page

Special features in the asymptotic expression of the electromagnetic spectrum from dipole which free fall into a Schwarzschild black hole

The characteristic features were found in the electromagnetic spectrum of radiation from free falling dipole, when it is fall radially into a Schwarzschild black hole. These features can be used as another method for the black hole mass determinating. Also, these features can be used for the determination some characteristics of the magnetosphere or the accretion disk around the black hole.Comment: 13 pages, 5 figure

Three-Dimensional Billiards with Time Machine

Self-collision of a non-relativistic classical point-like body, or particle, in the spacetime containing closed time-like curves (time-machine spacetime) is considered. A point-like body (particle) is an idealization of a small ideal elastic billiard ball. The known model of a time machine is used containing a wormhole leading to the past. If the body enters one of the mouths of the wormhole, it emerges from another mouth in an earlier time so that both the particle and its "incarnation" coexist during some time and may collide. Such self-collisions are considered in the case when the size of the body is much less than the radius of the mouth, and the latter is much less than the distance between the mouths. Three-dimensional configurations of trajectories with a self-collision are presented. Their dynamics is investigated in detail. Configurations corresponding to multiple wormhole traversals are discussed. It is shown that, for each world line describing self-collision of a particle, dynamically equivalent configurations exist in which the particle collides not with itself but with an identical particle having a closed trajectory (Jinnee of Time Machine).Comment: 20 pages (LATEX), 5 figures (EPS

Why Expenses are not Charges?

The article considers problems of such economic categories, such as “expenses”, “charges” and “costs” disclosure, gives clear differentiation of these notions and proves that it is wrong to consider them synonym

Passage of radiation through wormholes

We investigate numerically the process of the passage of a radiation pulse through a wormhole and the subsequent evolution of the wormhole that is caused by the gravitational action of this pulse. The initial static wormhole is modeled by the spherically symmetrical Armendariz-Picon solution with zero mass. The radiation pulses are modeled by spherically symmetrical shells of self-gravitating massless scalar fields. We demonstrate that the compact signal propagates through the wormhole and investigate the dynamics of the fields in this process for both cases: collapse of the wormhole into the black hole and for the expanding wormhole.Comment: 18 Pages, 13 figures, minor typos corrected, updated reference

Silhouettes of wormholes traversed for radiation

The problem of the passage of light through the mouth of a zero-mass wormhole and the possibility of observing the objects from another asymptotically flat space-time through the mouth of a wormhole are considered. It is shown that an individual star can have several images and the fact that the image of a flat Lambertian screen has a complex brightness distribution for an observer located on the opposite side of the throat. Images of two such screens visible inside the silhouette of a massless wormhole and the distribution of radiation intensity in their images are constructed.Comment: 11 pages, 12 figure

An application of high-dimensional statistics to predictive modeling of grade variability

The economic viability of a mining project depends on its efficient exploration, which requires a prediction of worthwhile ore in a mine deposit. In this work, we apply the so-called LASSO methodology to estimate mineral concentration within unexplored areas. Our methodology outperforms traditional techniques not only in terms of logical consistency, but potentially also in costs reduction. Our approach is illustrated by a full source code listing and a detailed discussion of the advantages and limitations of our approach. © 2020 by the authors. Licensee MDPI, Basel, Switzerland