Related papers: Null Cones and Einstein's Equations in Minkowski S…
The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After…
Recently the neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity has been substantially resolved. Consistency requires that the flat metric's null cone be respected by the null cone of the…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…
It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation in a fiber bundle $E$ which can be expressed as a product of spatial eigenfunctions…
We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her…
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial…
One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The $\gamma$-metric is instead a vacuum solution of Einstein's gravity. These spacetimes have no horizon and possess a…
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A…
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear…
We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…