Related papers: Integrable and non-integrable structures in Einste…
It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy can be obtained as the dynamical equations of three-dimensional General Relativity with a negative cosmological constant. This geometrization of the AKNS system is…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a…
In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field…
The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two…
The existence or non-existence of Einstein metrics on 4-manifolds with non-trivial fundamental group and the relation with the underlying differential structure are analyzed. For most points $(n,m)$ in a large region of the integer lattice,…
As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We classify Einstein metrics on $\mathbb{R}^4$ invariant under a four-dimensional group of isometries including a principal action of the Heisenberg group. The metrics are either Ricci-flat or of negative Ricci curvature. We show that all…
In this paper, three things are done. First, we study from an algebraic point of view the infinite-dimensional BMS-like extensions of the Carroll algebra relevant to the asymptotic structure of the electric and magnetic Carrollian limits of…
We show that combinations of (in general, non-linear) 2- and 3-form fields analogous to the Maxwell (1-form) field, completely describe perfect fluids, including the rotating ones. In the non-rotating case, the 2-form field in sufficient,…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
We introduce a new class of inhomogeneous cosmological models as solutions to the Einstein-Maxwell equations in electrovacuum. The new models can be considered to be nonlinear perturbations, through an electromagnetic field, of the…
Summary of abstract Field theory models including gauge theories with SSB are presented where the energy density of the true vacuum state (TVS) is zero without fine tuning. The above models are constructed in the gravitational theory where…
We consider the 4+1 Einstein's field equations (EFE's) in vacuum, simplified by the assumption that there is a four-dimensional sub-manifold on which an isometry group of dimension four acts simply transitive. In particular we consider the…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We investigate energy bounds and the stability of stationary asymptotically flat spacetimes with an ergoregion and no future horizon in the context of Einstein-Maxwell-Scalar field models which naturally arise in Kaluza-Klein and String…