Related papers: Truncation of Einstein equations through Gravitati…
We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details…
The action of recently proposed formulation of Einstein Theory of Gravitation is written according to 3+1 decomposition of the space-time variables. The result coincides with known formulation of Dirac and Arnowitt-Deser-Misner.
We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
In this article, we consider a special case of Metric-Affine f(R)-gravity for f(R) = R, i.e. the Metric-Affine General Relativity (MAGR). As a companion to the first article in the series, we perform the (3+1) decomposition to the…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We present the 3+1 decomposition of the Simon-Mars tensor, which has the property of being identically zero for a vacuum and asymptotically flat spacetime if and only if the latter is locally isometric to the Kerr spacetime. Using this…
We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly…
We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution…
The manuscript studies a 3+N+1-dimensional space in which the N extra dimensions are dynamically compact. The 3 large dimensions, behaving as the spacial part of the FRW metric, possess a different scale factor in comparison with the N…
The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the ``acceleration equals force" equation and…
We study a massless real self-interacting scalar field $\varphi$ non-minimally coupled to Einstein gravity with torsion in (2+1) space-time dimensions in the presence of cosmological constant. The field equations with a self-interaction…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus…
A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It…
We study an analytical solution to the Einstein's equations in 2+1-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this…
Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…
Strictly respecting the Einstein equations and supposing space-time is a medium, we derive the deformation of this medium by gravity. We derive the deformation in case of infinite plane, Robertson-Walker manifold, Schwarzschild manifold and…
Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multi-facetted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…