An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which M. Miller and Brewin have shown that the full field equations are much more restrictive than Einstein’s in ...

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behavio...

A holographic theory on N is described by a holographic dual theory on the boundary of N with action S, an integral over the boundary of N . Thus, in the limit of a vanishing boundary, the action of the holographic dual is S = 0, the action of a topological field theory. So, if general relativity is holographic, then when formulated on M a manifold without boundary it must be topological. In th...

After reviewing various interpretations of structural realism, I adopt here a definition that allows both relations between things that are already individuated (which I call “relations between things”) and relations that individuate previously un-individuated entities (”things between relations”). Since both space-time points in general relativity and elementary particles in quantum theory fal...

Einstein offered the principle of general covariance as the fundamental physical principle of his general theory of relativity and as responsible for extending the principle of relativity to accelerated motion. This view was disputed almost immediately with the counter-claim that the principle was no relativity principle and was physically vacuous. The disagreement persists today. This article ...

We describe a theory of gravitation on canonical noncommutative spacetimes. The construction is based on θ-twisted General Coordinate Transformations and Local Lorentz Invariance. 1. It can be suspected from various arguments, e.g. related with short-distance divergences in quantum field theory and singularities in General Relativity, that the classical concept of spacetime continuum breaks dow...