Related papers: Geometrodynamics: Spacetime or Space ?
The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self…
The geometrodynamics of the four-dimensional Einstein and Einstein-Maxwell theories were first studied by Wheeler and Misner more than fifty years ago, by constructing solutions of the constraints on an initial spatial slice in a…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Effective gravitational field theories with background fields break local Lorentz symmetry and diffeomorphism invariance. Examples include Chern-Simons gravity, massive gravity, and the Standard-Model Extension (SME). The physical…
We analyze some extensions of General Relativity. Within the framework of modified gravity, the Newtonian limit of a class of gravitational actions is discussed on the basis of the corresponding scalar-tensor model. For a generalized…
A retrospective analysis of the field theory of gravitation, describing gravitational field in the same way as other fields of matter in the flat space-time, is done. The field approach could be called "quantum gravidynamics" to distinguish…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
Arguments are made in favor of broadening the scope of the various approaches to splitting spacetime into a single common framework in which measured quantities, derivative operations, and adapted coordinate systems are clearly understood…
A set of new exact analytical General Relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate 1) a static non-empty space-time with a horizon-type singular surface; 2) time-dependent spatially…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specfiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
In this paper, we derive the Einstein's field equation (EFE) by considering an non-commuting two dimensional quantized space, which can be excited by absorbing energy. Any variation of the energy level of space quantas, will result in a…
Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a missing cardinal link to unification of all physical interactions. Problems of the…