Related papers: Unit-Lapse Forms of Various Spacetimes
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomporphisms and local spatial conformal transformations. In this paper we extend the construction of Shape…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…
Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ``spacetime''. His general theory of relativity further taught us that spacetime is not just a stage on…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
General Relativity assumes that spacetime is fully described by the metric alone. An alternative is the so called Palatini formalism where the metric and the connections are taken as independent quantities. The metric-affine theory of…
It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field…
The nature of the change in perspective that accompanies the proposal of a unified physical theory deriving from the single dimension of time is elaborated. On expressing a temporal interval in a multi-dimensional form, via a direct…
The relativity of cosmic time is developed within the framework of Cosmological Relativity in five dimensions of space, time and velocity. A general linearized metric element is defined to have the form $ds^2 = (1+\phi) c^2 dt^2 - dr^2 +…
This paper outlines a possibility for spacetime dynamics and structure, without postulating a metric ab initio. In this model, the closer an object is to a mass or energy source, the more paths through spacetime might be available to the…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
Gravitational waves and cosmic expansion are both described in terms of Einstein's general relativity. This article explores the similarities between the two phenomena, as well as some differences, using the fundamental concept of the…
Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly…
Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.