We derive a transformation from the usual ADM metric-extrinsic curvature variables on the phase space of Schwarzschild black holes, to new canonical variables which have the interpretation of Kruskal coordinates. We explicitly show that this transformation is non-singular, even at the horizon. The constraints of the theory simplify in terms of the new canonical variables and are equivalent to t...

We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n, 2) ordered by inclusion. For given k, ` (k < `) and m the problem is to find a family of size m in the set of `-subspaces of PG (n, 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O1 and O2 on the set of `-subspaces, and prove that the first m of them, ...

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...