We discuss how to construct the full Schwarzschild (Kruskal-Szekeres) spacetime in one swoop by using the bundle of orthonormal Lorentz frames and the Einstein equation without the use of coordinates. We never have to write down the Kruskal-Szekeres or an equivalent form of the metric. email: [email protected]

Abstract Understanding the missing matter problem in cosmological phenomena and scales of astrophysical is usually studied by modifying general relativity theory. In this article, we formulated Kruskal-Szekeres coordinate vacuum modified gravity model f ( R ) The generalization field equation was obtained generalizing Hilbert-Einstein’s action with gravitational Lagrangian terms (r) function. B...

Graph theory is one part of the branch mathematics that now very famous in computer design. The substitution a graph an object statement referred to as noktah, circle or point, and relationship line. applied various scientific disciplines, for example: economics, genetic psychology, operation research network optimization (telecommunication network, PLN transmission (electricity PDAM water dist...

We show how to embed spacelike slices of the Schwarzschild wormhole (or Einstein-Rosen bridge) in R 3. Graphical images of embeddings are given, including depictions of the dynamics of this nontraversable wormhole at constant Kruskal times up to, and beyond, the " pinching off " at Kruskal times ±1.

The radial, oscillatory motion of the Earth’s magnetopause has been found to occur predominantly with some distinct, sometimes called “magic” frequencies, which have been attributed to magnetospheric wave guide modes, typical solar wind variations or, more recently, surface waves on the magnetopause standing between the northern and southern ionospheres. In this paper we present for the first t...

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties ...

The Goodman–Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy p-value. The applicability ...