Related papers: A new geometric invariant on initial data for Eins…
Associated to analytic Hamiltonian vector fields in $\mathbb{C}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two universal constants that are invariant with respect to local analytic symplectic…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric.…
We obtain new invariant Einstein metrics on the compact Lie group $\SU(N)$ which are not naturally reductive. This is achieved by using the generalized flag manifold $G/K=\SU(k_1+\cdots +k_p)/\s(\U(k_1)\times\cdots\times\U(k_p))$ and by…
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…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying…
We propose a coordinate-invariant geometric formulation of the GENERIC stochastic differential equation, unifying reversible Hamiltonian and irreversible dissipative dynamics within a differential-geometric framework. Our construction…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
In this article a new stationary cylindrically symmetric solution of the Einstein's field equations with cosmological constant and Time machine is given. The garavitational field is created by ideal liquid with three massless scalar fields…
Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and…
The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are…