Related papers: Generalized de Sitter Space in $n$-dimensional Min…
Explicit time-dependent solutions of the 10D vacuum Einstein equations are found for which spacetime is compactified on six-dimensional warped spaces. We explicitly work out an example where the internal manifold is a six-dimensional…
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…
Morrow-Jones and Witt have shown that generic spatial topologies admit initial data that evolve to locally de Sitter spacetimes under Einstein's equations. We simplify their arguments, make them a little more general, and solve for the…
Quantum gravity is expected to contain descriptions of semiclassical spacetime geometries in quantum superpositions. To date, no framework for modelling such superpositions has been devised. Here, we provide a new phenomenological…
We consider a time-dependent $\mathcal{O}(1/G)$ deformation of pure de Sitter (dS) space in dS gravity coupled to a massless scalar field. It is the dS counterpart of the AdS Janus deformation and interpolates two asymptotically dS spaces…
Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with $\Lambda>0$, which admit a regular past and/or future…
We consider a complete, totally umbilical hypersurface $M$ of Riemannian space $(\hat{R}^n, \hat{g})$ induced by a Minkowski space $(R^n, F)$. Under certain conditions we prove that $M$ is isometric to a "round" hypersphere of the $(n +…
In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor…
We obtain a general class of time-dependent, asymptotically de Sitter backgrounds which solve the first order bosonic equations that extremize the action for supergravity with gauged non-compact $R$-symmetry. These backgrounds correspond…
Within the paradigm of non-perturbative Einstein gravity we study continuous curvature manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds could represent the spacetime of rotating gravastars or other similar…
In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are…
We derive a general integral formula on an embedded hypersurface for general relativistic space-times. Suppose the hypersurface is foliated by two-dimensional compact ``sections'' $S_s$. Then the formula relates the rate of change of the…
Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras…
Assuming both that our Universe is evolving into a de Sitter space and a vanishing cosmological constant, leaves only the option that the observed acceleration is provided by a "kinetic" energy of a scalar field. From an effective field…
We define 1+1 dimensional de Sitter manifold in this paper and we consider various coordinate systems on it. Some interesting aspects of the general theory of relativity are demonstrated by using the transformations between the considered…
Perturbative gravity in global de Sitter space is subject to so-called linearization stability constraints: If they are to couple consistently to the gravitational field, quantum states must be invariant under the de Sitter isometries.…
We study spacelike entire constant mean curvature hypersurfaces in Anti-de Sitter space of any dimension. First, we give a classification result with respect to their asymptotic boundary, namely we show that every admissible sphere…
Building upon the work of Brendle, Marques and Neves on the construction of counterexamples to Min-Oo's conjecture, we exhibit deformations of the de Sitter-Schwarzschild space of dimension $n\geq 3$ satisfying the dominant energy condition…
Let $M$ be a globally hyperbolic maximal compact $3$-dimensional spacetime locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well known that $M$ admits a unique foliation by constant mean curvature surfaces. In this…