相关论文: A note on the existence of standard splittings for…

The null splitting theorem (proved in math.DG/9909158) is discussed. As an application, a uniqueness theorem for Minkowski space and for de Sitter space associated with the occurrence of null lines (inextendible globally achronal null…

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…

This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes…

A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…

Given a globally hyperbolic spacetime $M$, we show the existence of a {\em smooth spacelike} Cauchy hypersurface $S$ and, thus, a global diffeomorphism between $M$ and $\R \times S$.

Spacetimes which are conformally related to reducible 1+3 spacetimes are considered. We classify these spacetimes according to the conformal algebra of the underlying reducible spacetime, giving in each case canonical expressions for the…

The topology of the causal boundary for standard static spacetimes--spacetimes time-invariantly conformal to a metric product of the Lorentz line and a Riemannian manifold--is studied in depth. As this is given in terms of a set of…

In a recent paper, we proved that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the…

We prove the existence of a Hawking Killing vector-field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth vacuum Einstein space-time. We do not assume analyticity of the space-time. This…

Let $G$ be a Lie group, and let $(M,\omega)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,\omega)$ with momentum map $\mu$, then $M$, the zero-level set of $\mu$, the orbit space, and the corresponding symplectic…

We extend the following result of Cochran ``A closed $m$-quasi Einstein manifold ($M,g,X$) with $m \ne -2$ has constant scalar curvature if and only if $X$ is Killing" covering the missing accidental case $m=-2$ and generalize it showing…

This paper continues the investigation of constant mean curvature (CMC) time functions in maximal globally hyperbolic spatially compact spacetimes of constant sectional curvature, which was started in math.DG/0604486. In that paper, the…

We investigate the spacetime of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write…

We prove an analogue of Miller's stable splitting of the unitary group $U(m)$ for spaces of commuting elements in $U(m)$. After inverting $m!$, the space $\text{Hom}(\mathbb{Z}^n,U(m))$ splits stably as a wedge of Thom-like spaces of…

In this paper we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case the component of any…

In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients…

In this work, we study the existence of gradient (proper) CKVs in locally rotationally symmetric spacetimes (LRS), those CKVs in the space spanned by the tangent to observers' congruence and the preferred spatial direction, allowing us to…

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse…

The gravitational collapse of a spherical distribution, in a class of f(R) theories of gravity, where f(R) is power function of R, is discussed. The spacetime is assumed to admit a homothetic Killing vector. In the collapsing modes, some of…

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…