Related papers: A Construct of Dynamics, Space and Gravity from Lo…
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.…
We present here a product between vectors and scalars that {\it mixes} them within their own space, using imaginaries to describe geometric products between vectors as complex vectors, rather than introducing higher order/dimensional vector…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
We give a derivation of general relativity and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace with two key properties. The first is…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We consider the Regge-Teitelboim model for a relativistic extended object embedded in a fixed background Minkowski spacetime, in which the dynamics is determined by an action proportional to the integral of the scalar curvature of the…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
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…
It is proposed that gravity may arise in the low energy limit of a model of matter fields defined on a special kind of a dynamical random lattice. Time is discretized into regular intervals, whereas the discretization of space is random and…
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically,…
Here show that, pure affine actions based solely on the Riemann curvature tensor lead to Einstein field equations for gravitation. The matter and radiation involved are general enough to impose no restrictions on material dynamics or vacuum…
We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…