Related papers: Precis of General Relativity
Nonunitary versions of Newtonian gravity leading to wavefunction localization admit natural special-relativistic generalizations. They include the first consistent relativistic localization models. At variance with the unified model of…
In general relativity, only relative acceleration has an observer-independend meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We derive the equations governing both…
In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally…
We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform…
The concept of velocity dependent mass, relativistic mass, is examined and is found to be inconsistent with the geometrical formulation of special relativity. This is not a novel result; however, many continue to use this concept and some…
Recent experiments have successfully tested Einstein's general theory of relativity to remarkable precision. We discuss recent progress in the tests of relativistic gravity in the solar system and present motivations for the new generation…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free…
In this paper we shall analyse the structure of the Cauchy Problem (CP briefly) for General Relativity (GR briefly) by applying the theory of first order symmetric hyperbolic systems.
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker and in McVittie spacetimes. The leading order corrections of the so-determined…
An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the…
Based on the consideration of naturalness and physical facts in Einstein's theories of relativity, a nontrivial spacetime physical picture, which has a slight difference from the standard one, is introduced by making a further distinction…
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to…
The aim of the present article is to give an exact and correct representation of the essentially important part of modern special relativity theory that touches upon the behavior of the proper length of accelerated moving bodies.In…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are…
We present a basics of the Einstein General Theory of Relativity. In the first part of this review we derive relations of Riemann geometry which are used in the General Relativity. In the second part we discuss Einstein Equations and some…
We set up a trace formula for the relativistic density of states in terms of a topological sum of classical periodic orbits. The result is applicable to any relativistic integrable system.
Uncertainties in the satellite world lines lead to dominant positioning errors. In the present work, using the approach presented in \cite{neu14}, a new analysis of these errors is developed inside a great region surrounding Earth. This…