Related papers: Gravity and Complexity
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
A specific theoretical framework is important for designing and conducting an experiment, and for interpretation of its results. The field of gravitational physics is expanding, and more clarity is needed. It appears that some popular…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
In $f(T)$ gravity, the theory modifies the gravitational action by introducing a function of the torsion scalar $T$. This approach allows for a different treatment of gravity than general relativity, particularly in cosmological contexts.…
Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks…
Motivated on the one hand by recent results on isochronous dynamical systems, and on the other by quantum gravity applications of complex metrics, we show that, if such enlarged class of metrics is considered, one can easily obtain periodic…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems…
According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
The basic equations describing a Newtonian universe with uniform pressure are reexamined. We argue that in the semi-classical formulation adopted in the literature the continuity equation has a misleading pressure gradient term. When this…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
Bianchi I cosmological solutions in f(T) gravity are discussed. We start from diagonal metrics and tetrads and show that their dynamical equations are pretty much tractable analytically, with a possible arena for physical applications. Then…
The studies of the generalized Einstein Lagrangian densities without torsion are extended to those of the more generalized Lagrangian densities with torsion. The properties of the more generalized Lagrangian densities are studied…