Related papers: A classification theorem for compact Cauchy horizo…
The famous Hopf-Rinow Theorem states, amongst others, that a Riemannian manifold is metrically complete if and only if it is geodesically complete. The Clifton-Pohl torus fails to be geodesically complete proving that this theorem cannot be…
Gott recently has constructed a spacetime modeled by two infinitely long, parallel cosmic strings which pass and gravitationally interact with each other. For large enough velocity, the spacetime will contain closed timelike curves. An…
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…
Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…
Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner-Nordstr\"om…
It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the…
We prove a Goldberg-Sachs theorem in dimension three. To be precise, given a three-dimensional Lorentzian manifold satisfying the topological massive gravity equations, we provide necessary and sufficient conditions on the tracefree Ricci…
We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the…
We consider the fluid dual of $(d+2)$-dimensional vacuum Einstein equation either with or without a cosmological constant. The background solutions admit black hole event horizons and the spatial sections of the horizons are conformally…
We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In…
We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner-Nordstr\"om (asymptotically flat, de Sitter or anti-de Sitter) spacetime, whose restrictions to the event horizon have compact…
On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show…
We investigate quasilocal horizons in inhomogeneous cosmological models, specifically concentrating on the notion of a trapping horizon defined by Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate and analyse…
We prove that, among all (n + 1)-dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing hori-zons have minimal modes for the Dirac operator. As a…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak…
Galego and Samuel showed that if $K,L$ are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is $c_0$-saturated if and only if it is subprojective if and only if $K$ and $L$ are both scattered. We remove the…
The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a K\"ahler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A…