Related papers: Phase Spaces in Special Relativity: Towards Elimin…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
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…
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its…
In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
Special relativity calculates, by means of the Lorentz gamma factor, the proper time of all inertial systems from the observer proper time, which is taken as a time standard. So, any temporal inference relies in first instance on the…
An approach is developed which enables one to analyze gravitational effects without usage of any concrete model of geometry (or a class of models of geometry) of space-time and even without any coordinate system. Instead, the formalism of…
Starting from the canonical phase space for discretised (4d) BF-theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection…
Within the framework of projective geometry, we investigate kinematics and symmetry in $(\alpha,\beta)$ spacetime-one special types of Finsler spacetime. The projectively flat $(\alpha,\beta)$ spacetime with constant flag curvature is…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
In my previous work, physics/0205011, I reported several observations on special relativity, its experimental facts and its relations to quantum mechanics and statistical mechanics. These observations made us conscious: Special relativity…
We show that a two twistor phase space {\`a} priori describing two non localized massless and spinning particles may be decomposed into a product of three independent phase spaces: the (forward) cotangent bundle of the Minkowski space, the…
We develop a comprehensive cosmological framework based on the principle that our universe originated as a three-dimensional spatial configuration governed purely by energy functionals, with time emerging dynamically through quantum loop…
We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified…
We show that a number of problems of modern cosmology may be solved in the framework of multidimensional gravity with high-order curvature invariants, without invoking other fields. We use a method employing a slow-change approximation,…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…
Minkowski spacetime can be mapped by a series of projections in a higher-dimensional spacetime to a Euclidean space, constituting a process of Euclideanization shown here in detail for two dimensions. The result allows regularizations and…
We employ a twist deformation of infinitesimal diffeomorphisms to construct a modification of General Relativity on a non-commutative spacetime extending the local kappa-Minkowski geometry. This spacetime arises in Deformed Special…