Related papers: Fractal Relativity, Generalized Noether Theorem an…
In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light…
Noether's theory offers us a useful tool to research the conserved quantities and symmetries of the modified gravity theories, among which the $f(T)$ theory, a generally modified teleparallel gravity, has been proposed to account for the…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
Il is argued that the generalisation of the mechanical principles to other variables than localisation, velocity and momentum leads to the laws of generalized dynamics under the condition of continuous and derivable space time. However,…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
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.…
While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by…
We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical…
The Standard Model plus gravitation is derived from general relativity with three dimensions of time. I claim that when the Lagrangian for general relativity is calculated using three dimensions of time, the unified field theory results. I…
It is a remarkable fact that all processes occurring in the observable Universe are irreversible, whereas the equations through which the fundamental laws of physics are formulated are invariant under time reversal. The emergence of…
General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the…
In this work we consider a scale-tensor theory in which the space-time is endowed with a Weyl integrable geometrical structure due to the Palatini variational method. Since the scalar field has a geometrical nature (related to…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of…
This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…
Discrepancies between observations at early and late cosmic epochs, and the vacuum energy problem associated with the interpretation of cosmological constant, are questioning the $\Lambda$CDM model. Motivated by these conceptual and…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
From the constructions of the quantum spacetime, a four dimensional quantized spacetime can be embedded in a five dimensional continuous spacetime. Thus to observe from the five dimensional continuous spacetime where the four dimensional…