Related papers: Collapsing in the Einstein flow
We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated to regions bounded by them. This realizes crucial elements of the general boundary…
We prove that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single non-expanding null surface belongs to family of the near (extremal)…
Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
Conformally invariant GUT-like model including gravity based on Riemann - Cartan space-time $U_4$ is considered. Cosmological scenario that follows from the model is discussed and standard quantum gravitational formalism in the…
We show that in theories of gravity that add quadratic curvature invariants to the Einstein-Hilbert action there exist expanding vacuum cosmologies with positive cosmological constant which do not approach the de Sitter universe. Exact…
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data…
Using the implicit function theorem, we prove existence of solutions of the so-called conformally covariant split system on compact 3-dimensional Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC) vacuum initial…
We study the properties of spacelike singularities in spherically symmetric spacetimes obeying the Einstein equations, in the presence of matter. We consider in particular matter described by a scalar field, both in the presence of an…
This work investigates some global questions about cosmological spacetimes with two dimensional spherical, plane and hyperbolic symmetry containing matter. The result is, that these spacetimes admit a global foliation by prescribed mean…
Multidimensional cosmological model describing the evolution of one Einstein space of non-zero curvature and n Ricci-flat internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric forms. When forms…
The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically…
In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the…
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions.…
The $C^3$ approach is an invariant formalism that utilizes the eigenvalues of the Riemann curvature tensor to match spacetimes across a specific matching surface. We apply this approach to match an anisotropic fluid with an exterior vacuum…
We find classical solutions of two dimensional noncritical string theory which give rise to geometries with spacelike boundaries, similar to spacetimes with cosmological event horizons. In the c=1 matrix model, these solutions have a…
We recently described a cosmological quantum spacetime of vanishing spatial curvature, which can be considered as background for the IKKT matrix model, assuming that the resulting gauge theory couples weakly. Building on this example, we…
In this paper, we investigate the mean curvature flows starting from all non-minimal leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean…
In this paper, we first investigate the flow of convex surfaces in the space form $\mathbb{R}^3(\kappa)~(\kappa=0,1,-1)$ expanding by $F^{-\alpha}$, where $F$ is a smooth, symmetric, increasing and homogeneous of degree one function of the…
Conformal mappings of surfaces of constant mean curvature onto compact bounded background spaces are constructed for Minkowski space-time and for Schwarzschild black hole spacetimes. In the black hole example, it is found that initial data…