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We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
The cosmology of metric-affine gravity is studied for the general, parity preserving action quadratic in curvature, torsion and non-metricity. The model contains 27 a priori independent couplings in addition to the Einstein constant. Linear…
The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
The present work is a natural continuation of the previous paper arXiv:0911.5597. In this work, within the scope of the Generalized Uncertainty Principle, a model of the high energy deformation for a particular case of Einstein's equations…
We argue that generic off-diagonal vacuum and nonvacuum solutions for Einstein manifolds mimic physical effects in modified gravity theories (MGTs) and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical Lorentz…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…
In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined…
The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic Einstein-Hilbert action in terms of these fields as well as the harmonic…
We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. "Einstein-aether theory". The classical solutions of this theory in two dimensions depend on one coupling constant. When this…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…
Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of an renormalizable effective density matrix and…
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
We study the thermodynamics of Einstein gravity with vanishing cosmological constant subjected to conformal boundary conditions. Our focus is on comparing the series of subextensive terms to predictions from thermal effective field theory,…
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames…
Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
We utilize the gravitational decoupling via the extended geometric deformation to extend the Schwarzschild vacuum solution to new black holes in Rastall theory. By employing linear transformations that deform both the temporal and radial…