Related papers: Dynamically generated embeddings of spacetime

We show that the description of the space-time of general relativity as a diagonal four dimensional submanifold immersed in an eight dimensional hypercomplex manifold, in torsionless case, leads to a geometrical origin of the cosmological…

We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…

We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…

Vanishing of the Fefferman-Graham obstruction tensor was used by Andersson and Chru{\'s}ciel to show stability of the asymptotically de Sitter spaces in even dimensions. However, existing proofs of hyperbolicity of this equation contain…

Recent astronomical observations strongly indicate that the current Universe is undergoing an accelerated phase of expansion. The discovery of this fact was unexpected and resulted in the comeback of cosmological constant. The conception of…

The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding…

We show existence and uniqueness for timelike minimal submanifolds (world volume of p-branes) in ambient Lorentz manifolds admitting a time function in a neighborhood of the initial submanifold. The initial value formulation introduced and…

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the…

We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological…

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the…

In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…

I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…

It is suggested, that a curved 4-dimensional space-time manifold is a strained elastic plate in multidimensional embedding space-time. Its thicknesses along extradimensions are much less than 4-dimensional sizes. Reduced 4-dimensional free…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…

A temporal network -- a collection of snapshots recording the evolution of a network whose links appear and disappear dynamically -- can be interpreted as a trajectory in graph space. In order to characterize the complex dynamics of such…

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…

The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…

We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge…