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The problem of constructing a model of an extended charged particle within the context of general relativity has a long and distinguished history. The distinctive feature of these models is that, in some way or another, they require the…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness…
Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…
We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with…
The classical Busemann-Petty problem asks whether smaller central hyperplane sections of origin-symmetric convex bodies necessarily imply smaller total volume. Zvavitch studied this question for arbitrary measures with continuous even…
We construct exact initial data for closed cosmological models filled with regularly arranged black holes in the presence of $\Lambda$. The intrinsic geometry of the 3-dimensional space described by this data is a sum of simple closed-form…
We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and…
This contribution inquires into Clausius' proposal that "the entropy of the world tends to a maximum.'" The question is raised whether the entropy of "the world" actually does have a maximum; and if the answer is "Yes!," what such states of…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
We consider new models of dark energy with finite time future singularities, by introducing the pressure density as a function of the scale factor. This approach gives acceptable phenomenological models of dark energy, practically…
Recent experimental results from supernovae Ia observations have been interpreted to show that the rate of expansion of the universe is increasing. Other recent experimental results find strong indications that the universe is ``flat.'' In…
We present a time-dependent uniform-density interior Schwarzschild solution, an exact solution to the Einstein field equations. Our solution describes the collapse (or the time-reversed expansion) of an object from an infinite radius to an…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
The problem of constructing global models describing isolated axially symmetric rotating bodies in equilibrium is analyzed. It is claimed that, whenever the global spacetime is constructed by giving boundary data on the limiting surface of…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…