Related papers: $3$-dimensional complete vacuum static spaces
We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. In this setting, under suitable constraints on the behavior of…
In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices,…
We show that the space of metrics of positive scalar curvature on any 3-manifold is either empty or contractible. Second, we show that the diffeomorphism group of every 3-dimensional spherical space form deformation retracts to its isometry…
In the spirit of the Newtonian theory, we characterize spherically symmetric empty space in general relativity in terms of energy density measured by a static observer and convergence density experienced by null and timelike congruences. It…
We show that a tensor product of four specific $1{+}2$ Minkowski vacuum states is a self-consistent vacuum state for an infinite set of three-dimensional anti-de Sitter (AdS$_3$) spacetimes if their parity and time-reversal symmetry are…
We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions…
In the study of immersed surfaces of constant positive extrinsic curvature in space-forms, it is natural to substitute completeness for a weaker property, which we here call quasicompleteness. We determine the global geometry of such…
We investigate the details of the canonical quantization of effective quantum field theories in anti-de Sitter spacetime, emphasizing the stability of the quantum vacuum. We take the scalar and Maxwell fields as examples. For the…
We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $\Lambda<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static…
A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum…
Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is…
The problem of the stabilization of moduli is discussed within the context of compactified strongly coupled heterotic string theory. It is shown that all geometric, vector bundle and five-brane moduli are completely fixed, within a…
We investigated the cosmology in a higher-curvature gravity where the dimensionality of spacetime gives rise to only quantitative difference, contrary to Einstein gravity. We found exponential type solutions for flat isotropic and…
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost…
We sketch the construction of a quantum model of 3 dimensional de Sitter space, based on the Covariant Entropy Principle and the observation that semi-classical physics suggests the possibility of a consistent theory of a finite number of…
Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
In this paper, we completely classify $3$-dimensional complete self-shrinkers with constant norm $S$ of the second fundamental form and constant $f_{3}$ in Euclidean space $\mathbb R^{4}$, where $h_{ij}$ are components of the second…
We analyze the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D>3, all these theories admit a maximally supersymmetric…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…