Related papers: Is the Regge Calculus a consistent approximation t…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
It is commonly remarked that contemporary physics faces a challenge in reconciling quantum theory with Relativity, specifically General Relativity as a theory of gravity. But "challenge" is too mild a descriptor. Once one understands both…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the…
A central question in General Relativity (GR) is how to determine whether singularities are geometrical properties of spacetime, or simply anomalies of a coordinate system used to parameterize the spacetime. In particular, it is an open…
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…
General Relativity is considered to be so far the best gravitation theory. However it is quite hard to use in real situations. The root of these difficulties lays in the non-linearity of the theory. Our aim was not to linearize the theory,…
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent extension to Lorentzian metrics of low regularity. The latter is motivated by the quest to…
An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise…
A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.
We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal…
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…
Current tests of General Relativity are performed using approximations which neglect a key feature of complete solution of Einstein's theory: higher-order modes. Our analysis will reassess these tests, including these higher-order mode…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
We give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure…
Among relativistic theories of gravitation the closest ones to general relativity are the scalar-tensor ones and these with Lagrangians being any function f(R) of the curvature scalar. A complete chart of relationships between these…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…