相关论文: Generalised hyperbolicity in singular space-times

The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…

We consider hyperbolic toral automorphisms which are reversible with respect to a linear area-preserving involution. We will prove that within this context reversibility is linked to a generalized Pell equation whose solutions we will…

Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…

Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foliations of this kind in…

We argue that special and general theories of relativity implicitly assume spacetime events correspond to quantum measurement outcomes. This leads to a change in how one should view the equivalence of spacetime and gravity. We describe a…

In this paper we prove the conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily…

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…

We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the…

We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…

A new cosmological object in analogy with the concept of a wormhole in general relativity is introduced. As wormholes connect two distant points through a tunnel in spacetime, this new object connects two spacetime through a large mouth…

The global structure of 2-dimensional dilaton gravity is studied, attending in particular to black holes and singularities. A gravitational energy is defined and shown to be positive at spatial singularities and negative at temporal…

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.

This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures…

We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.

Using the framework of Colombeau algebras of generalized functions, we prove the existence and uniqueness results for global generalized solvability of semilinear hyperbolic systems with nonlinear nonlocal boundary conditions. We admit…

Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power…

The influential theorems of Hawking and Penrose demonstrate that spacetime singularities are ubiquitous features of general relativity, Einstein's theory of gravity. The utility of classical general relativity in describing gravitational…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…